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Question: \(\overrightarrow{A} = 3\widehat{i} + 4\widehat{j} + 2\widehat{k},\overrightarrow{B} = 6\widehat{i} ...

A→=3i^+4j^+2k^,B→=6i^−j^+3k^\overrightarrow{A} = 3\widehat{i} + 4\widehat{j} + 2\widehat{k},\overrightarrow{B} = 6\widehat{i} - \widehat{j} + 3\widehat{k}. Find a vector parallel to A→\overrightarrow{A} whose magnitude is equal to that of B→\overrightarrow{B}.

A

(a)4629(3i^+4j^+2k^)\sqrt{\frac{46}{29}}\left( 3\widehat{i} + 4\widehat{j} + 2\widehat{k} \right)

A

(b)4629(6i^−j^+3k^)\sqrt{\frac{46}{29}}\left( 6\widehat{i} - \widehat{j} + 3\widehat{k} \right)

A

(c)2946(3i^+4j^+2k^)\sqrt{\frac{29}{46}}\left( 3\widehat{i} + 4\widehat{j} + 2\widehat{k} \right)

A

(d) None

Explanation

Solution

(a)

x→=A^∣B∣=(3i^+4j^+2k^)36+1+99+16+4\overrightarrow{x} = \widehat{A}|B| = \frac{\left( 3\widehat{i} + 4\widehat{j} + 2\widehat{k} \right)\sqrt{36 + 1 + 9}}{\sqrt{9 + 16 + 4}}=4629(3i^+4j^+2k^)\sqrt{\frac{46}{29}}\left( 3\widehat{i} + 4\widehat{j} + 2\widehat{k} \right)