A= 2i + 3j - k, B= 4i + 2j - 2k, Find a vector x parallel to A but has magnitude of B ?

Question

Answer is √12/7 (2i+3j) - K

solve it , i have mcat admission test please solve it

Answer 1

Magnitude of a vector is its length:

if v = ai + bj + ck
|v| = sqrt(a^2 + b^2 + c^2)
So that's the length. It's a scalar quantity.
|b| = sqrt(16+4+4) = sqrt(24)
|v| = |b|

Parallel vectors: the dot product is 0.
so. A.v = 0
or 2a + 3b - 1c = 0

The thing is there isn't just one answer. I'm guessing you set c to be -1 or something to get a -1k in your answer.

After that you have two equations with a and b left. (one with a and b the other with a^2 and b^2. Which has 2 answers).

It feels like there should be 1 more piece of information in the question to get a unique answer though.

Answer 2

Thanks sir, I understand that information is lacking but I don't know why they have given such high level question for MCAT admission test :/ , anyway thanks