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A=2i+pj+qk and B=5i+7j+3k.if vector A parallel vector B,then the values of p and q are, respectively a)

A=2i+pj+qk and B=5i+7j+3k.if vector A parallel vector B,then the values of p and q are, respectively a)

Grade:11

1 Answers

Shaswata Biswas
132 Points
7 years ago
{\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

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