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Question: There are two vectors \(\overrightarrow{A}\)= 2\(\widehat{i}\) + \(\widehat{j}\) + \(\widehat{k}\) a...

There are two vectors A→\overrightarrow{A}= 2i^\widehat{i} + j^\widehat{j} + k^\widehat{k} and

B→\overrightarrow{B} = i^\widehat{i} + 2j^\widehat{j} – 2k^\widehat{k} then component of A→\overrightarrow{A} along B→\overrightarrow{B} is –

A

29(i^+2j^−2k^)\frac{2}{9}(\widehat{i} + 2\widehat{j} - 2\widehat{k})

B

23(2i^+j^+k^)\frac{2}{3}(2\widehat{i} + \widehat{j} + \widehat{k})

C

23(i^+2j^−2k^)\frac{2}{3}(\widehat{i} + 2\widehat{j} - 2\widehat{k})

D

None of these

Answer

29(i^+2j^−2k^)\frac{2}{9}(\widehat{i} + 2\widehat{j} - 2\widehat{k})

Explanation

Solution

Component of A→\overrightarrow{A} along B→\overrightarrow{B}= A→.B→∣B→∣.B^\frac{\overrightarrow{A}.\overrightarrow{B}}{|\overrightarrow{B}|}.\widehat{B}