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Question: If \(\overset{\rightarrow}{A} = \widehat{i} + 2\widehat{j} + 2\widehat{k}\)and \(\overset{\rightarro...

If A→=i^+2j^+2k^\overset{\rightarrow}{A} = \widehat{i} + 2\widehat{j} + 2\widehat{k}and B→=3i^+6j^+2k^\overset{\rightarrow}{B} = 3\widehat{i} + 6\widehat{j} + 2\widehat{k}, then the vector in the direction of A→\overset{\rightarrow}{A}and having same magnitude as ∣B→∣|\overset{\rightarrow}{B}|, is –

A

(a)73(i^+2j^+2k^)\frac{7}{3}(\widehat{i} + 2\widehat{j} + 2\widehat{k})

A

(b)7(i^+2j^+2k^)7(\widehat{i} + 2\widehat{j} + 2\widehat{k})

A

(c)37(i^+2j^+2k^)\frac{3}{7}(\widehat{i} + 2\widehat{j} + 2\widehat{k})

A

(d)79(i^+2j^+2k^)\frac{7}{9}(\widehat{i} + 2\widehat{j} + 2\widehat{k})

Explanation

Solution

(a)

Vector in the direction of A→\overset{\rightarrow}{A} and having same magnitude as B is = BA^B\widehat{A}= B(A→A)B\left( \frac{\overset{\rightarrow}{A}}{A} \right)

= 73(i^+2j^+2k^)\frac{7}{3}(\widehat{i} + 2\widehat{j} + 2\widehat{k})