How do I find a vector that is perpendicular to 2 other vectors in 3d? (1 Viewer)

[Epicman69]

Just give me a general way I can't seem to figure one out lol. I know the cross product but I don't think I am allowed to actually use it in the HSC :C

 

[Run hard@thehsc]

Not too sure on this one, but I guess you can make the perpendicular vector be of the form (x1, y1, z1). Then create your first eq of the dot product involving the multiplication of the per vector and the first vector equalling zero. Then do the same for the second vector .... after which you could equate the respective components to solve for x1, y1 and z1

 

[5uckerberg]

Not too sure on this one, but I guess you can make the perpendicular vector be of the form (x1, y1, z1). Then create your first eq of the dot product involving the multiplication of the per vector and the first vector equalling zero. Then do the same for the second vector .... after which you could equate the respective components to solve for x1, y1 and z1 --- not sure if this is right tho....

Instead to find a vector that is perpendicular to two different vectors make one component in the vector zero eg let or or be zero and then you have to find the dot product between your vector and the two given vectors.[/TEX][/TEX][/TEX]

 

[Drongoski]

Just give me a general way I can't seem to figure one out lol. I know the cross product but I don't think I am allowed to actually use it in the HSC :C

Why would they set such a question if they do not teach you the cross product?

 

[Epicman69]

Why would they set such a question if they do not teach you the cross product?

Oh, this is from my tutoring so it may be out of the syllabus! Also, I do know the cross product, but not sure if I am allowed to use it in the HSC

 

[c_z_m]

Oh, this is from my tutoring so it may be out of the syllabus! Also, I do know the cross product, but not sure if I am allowed to use it in the HSC

You can't use the cross product as a means of working out for Section II questions (i.e: non-multiple choice questions)

You can use the cross product for multiple choice questions and as a means to verify your answer for Section II questions.

 

[Epicman69]

You can't use the cross product as a means of working out for Section II questions (i.e: non-multiple choice questions)

You can use the cross product for multiple choice questions and as a means to verify your answer for Section II questions.

yea that's what I thought, also would a question like this be in the 4 unit test?

 

[c_z_m]

yea that's what I thought, also would a question like this be in the 4 unit test?

There may very well be questions of perpendicularity in the 4U test. However, I doubt any would require you to use the cross-product - most of the time your textbook knowledge should suffice, rather than that of Dr Du or whatnot.

 

[c_z_m]

There may very well be questions of perpendicularity in the 4U test. However, I doubt any would require you to use the cross-product - most of the time your textbook knowledge should suffice, rather than that of Dr Du or whatnot.

Though, to add to my previous point, the cross product is always useful to have in your maths arsenal. It's not particularly hard to remember and in some cases can lead you to the answer (even if you can't get marks for using it). Don't stress too much if you can't remember it however.

 

[5uckerberg]

Though, to add to my previous point, the cross product is always useful to have in your maths arsenal. It's not particularly hard to remember and in some cases can lead you to the answer (even if you can't get marks for using it). Don't stress too much if you can't remember it however.

From experience, it is a very powerful method because all you gotta do is to cover one column except the direction with your finger. Works similarly to the Heaviside cover-up method for partial fractions.

 

[c_z_m]

From experience, it is a very powerful method because all you gotta do is to cover one column except the direction with your finger. Works similarly to the Heaviside cover-up method for partial fractions.

That's true. It's kind of stupid by the 4U syllabus writers not to include the cross product - the scope of Vectors questions are severely limited. Plus when dealing with perpendicularity you'll often have to take a longer route to get to the answer.

I remember an eventful Dr Du lesson where we did a question without the cross product and it took 30 minutes. With the cross product it took 2. Dr Du himself remarked, "HSC syllabus stupid."

 

[Epicman69]

That's true. It's kind of stupid by the 4U syllabus writers not to include the cross product - the scope of Vectors questions are severely limited. Plus when dealing with perpendicularity you'll often have to take a longer route to get to the answer.

I remember an eventful Dr Du lesson where we did a question without the cross product and it took 30 minutes. With the cross product it took 2. Dr Du himself remarked, "HSC syllabus stupid."

Hey bro what would your method be for these types of questions?

 

[c_z_m]

Hey bro what would your method be for these types of questions?

For Dr Du homework, it's almost always expected to use cross products. "Normal" vector methods would take too long.

For a school/HSC exam, I would let a vector, say v1, be (x1, y2, z3) and the others along the same lines. I would then use the dot product (which equals 0 for perpendicular vectors). If you want to find the intercepts of those points, rewrite your vectors in a different form, which should do the trick.

 

[5uckerberg]

That's true. It's kind of stupid by the 4U syllabus writers not to include the cross product - the scope of Vectors questions are severely limited. Plus when dealing with perpendicularity you'll often have to take a longer route to get to the answer.

I remember an eventful Dr Du lesson where we did a question without the cross product and it took 30 minutes. With the cross product it took 2. Dr Du himself remarked, "HSC syllabus stupid."

That's true. It's kind of stupid by the 4U syllabus writers not to include the cross product - the scope of Vectors questions are severely limited. Plus when dealing with perpendicularity you'll often have to take a longer route to get to the answer.

I remember an eventful Dr Du lesson where we did a question without the cross product and it took 30 minutes. With the cross product it took 2. Dr Du himself remarked, "HSC syllabus stupid."

My question is "Does Dr Du write the NSW syllabus?" and be realistic when people write the syllabus they want to make sure teachers can finish teaching all their content in a whole year. But yeah I can see why some people might ask for it.

I can also see why the cross product would be very useful here because if you are finding a vector that is perpendicular to the two other vectors the method I stated as shown would involve a lot of guesswork but using the cross product you destroy the guesswork because you know this vector through the cross product will be perpendicular to both of these products.

Instead to find a vector that is perpendicular to two different vectors make one component in the vector zero eg let or or be zero and then you have to find the dot product between your vector and the two given vectors.[/TEX][/TEX][/TEX]

 

[c_z_m]

Hey bro what would your method be for these types of questions?

For Dr Du homework, it's almost always expected to use cross products. "Normal" (syllabus approved) vector methods would take too long.

For a school/HSC exam, I would let a vector, say v1, be (x1, y2, z3) and the others along the same lines. I would then use the dot product (which equals 0 for perpendicular vectors). If you want to find the intercepts of those points, rewrite your vectors in a different form, which should do the trick.

 

[c_z_m]

My question is "Does Dr Du write the NSW syllabus?" and be realistic when people write the syllabus they want to make sure teachers can finish teaching all their content in a whole year. But yeah I can see why some people might ask for it.

I also recall Dr Du teaching Simpson's method for 3U, even though it was explicitly removed from the syllabus and formula sheet. I guess some tutoring centres like to go "outside the syllabus" as if that's a way to boost student marks.

 

[Epicman69]

I also recall Dr Du teaching Simpson's method for 3U, even though it was explicitly removed from the syllabus and formula sheet. I guess some tutoring centres like to go "outside the syllabus" as if that's a way to boost student marks.

yea they did lol I just disregarded those questions xd

 

[5uckerberg]

I also recall Dr Du teaching Simpson's method for 3U, even though it was explicitly removed from the syllabus and formula sheet. I guess some tutoring centres like to go "outside the syllabus" as if that's a way to boost student marks.

Wait Simpson’s method for 3U? I never seen that ever happen.

 

[c_z_m]

Wait Simpson’s method for 3U? I never seen that ever happen.

It was taught alongside the trapezoidal rule so it may have been a 2U thing - it was definitely taught in their 3U classes though. Still not a justification to be teaching that in my opinion.

 

[ExtremelyBoredUser]

Pretty sure Simpsons method used to be old syllabus for 2U from HSC past papers I've seen. I think its taught there since its a more accurate approximation than trapezoid rule but yeah its out of syllabus, you would only be expected to know Trapezium Rule. I'm not too sure if HSC markers are lenient towards out of syllabus methods though... but I've seen some teachers who don't mind out of syllabus methods so Dr Du might be trying to be helpful in that niche circumstance..? Or its just part of the brand/norm.