2004 STEP II Q6 Vector Qn

I am re-posting this question.

I tried to find vector Q using this way:

Since Q is parallel to q, I will only consider the components of a, b and c that perpendicular to a.

For a, there is no component that is parallel to q.

For b, the component parallel to q is b - 3a.

As b.c=2, this means the component of c parallel to b is (2/5)b.

Thus, for c, the component parallel to q is 2/5(b - 3a).

Adding up the components, Q = b - 3a + 2/5(b - 3a) = (7/5)b - (21/5)a.

However, I am not able to get the correct solution, which is Q = -(9/2)a + (3/2)b using the above mentioned method.

I understand there're other methods. But I'll like to know the problem with my method. Thanks.

2004 STEP II Q6.PNG30.7KB

Reply 1

DFranklin

18

I'm not clear what you mean by "the component of X parallel to Y", but I suspect the line:

"As b.c=2, this means the component of c parallel to b is (2/5)b."

is not correct.

Suppose c = 2b/25 (which might not make sense for the rest of the question - I'm just talking about the line in quotes).

Then b.c = 2(b.b)/25 = 2, so by the line above, the component of b parallel to 2b/25 is 2b/5, which I doubt is what you mean.

Reply 2

superkinetic

OP

Original post by DFranklin

I'm not clear what you mean by "the component of X parallel to Y", but I suspect the line:

"As b.c=2, this means the component of c parallel to b is (2/5)b."

is not correct.

Suppose c = 2b/25 (which might not make sense for the rest of the question - I'm just talking about the line in quotes).

Then b.c = 2(b.b)/25 = 2, so by the line above, the component of b parallel to 2b/25 is 2b/5, which I doubt is what you mean.

Thanks for pointing out. I mistook the length of projection of c on b, which is 2/5, as the component of c parallel to b.

But even if I take 2b/25, it does not lead to the correct solution. So what's the error here?