Question

vector A=2i+pj+qk, and vector B=5i+7j+3k. If  A || B, p and q are, respectively.​

Answer 1

Answer:

Everything in B will be 2.5 times everything in A because they are parallel and 5/2 = 2.5. So, p= 14/5 and q=6/5.

Explanation:

{\vec{A}} = 2 \widehat{i} + p\widehat{j} + q\widehat{k} and {\vec{B}} = 5 \widehat{i} + 7\widehat{j} + 3\widehat{k}.

Since they are parallel, |A×B| = 0

\implies \left | [2 \widehat{i} + p\widehat{j} + q\widehat{k}] \times [5 \widehat{i} + 7\widehat{j} + 3\widehat{k} ]\right | = 0

\implies \left | (3p-7q) \widehat{i} + (5q-6)\widehat{j} + (14-5p)\widehat{k}\right | = 0

So, (3p - 7q) = 0  ;  (5q - 6) = 0.   ;  (14 - 5p) = 0

Hence, p = \frac{14}{5}   &  q = \frac{6}{5}

THANKS

Answer 2

Answer:by using shortcut

Explanation:14/5 and 6/5