If two vectors A=ai−j−4k and B=2i−bj+3k and 3A=2B, what are the values of a and b?

sombereki51

sombereki51

Answered question

2022-09-19

If two vectors A = a i j 4 k and B = 2 i b j + 3 k and 3A=2B, what are the values of a and b?
I have tried to solve it by first calculating 3A and 2B. As these two vectors are equal their magnitudes should be equal too which gives me the equation
9 a 2 + 153 = 4 b 2 + 52 9 a 2 4 b 2 = 101 . . . . . . . ( 1 )
the answer in the book is given as a = 4 / 3 and b = 3 / 2. I think these two values should satisfy equation (1). But it doesn't. Can anyone verify if I am doing the math in the wrong way or the answers are wrong.

Answer & Explanation

Trace Arias

Trace Arias

Beginner2022-09-20Added 6 answers

Two vectors are equal if and only if each of their components is equal.
The condition 3A=2B is saying
3 a i 3 j 12 k = 4 i 2 b j + 6 k .
See that the k -component is not equal. A contradiction. Thus, there is no such a and b

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