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Question: There are two vectors \(\overset{\rightarrow}{A}\) = \(2\widehat{i}\) + \(\widehat{j}\) + \(\widehat...

There are two vectors A→\overset{\rightarrow}{A} = 2i^2\widehat{i} + j^\widehat{j} + k^\widehat{k} and B→\overset{\rightarrow}{B} = i^\widehat{i} + 2j^2\widehat{j} – 2k^2\widehat{k}, then vector component of A→\overset{\rightarrow}{A} along B→\overset{\rightarrow}{B} is –

A

2i^+2j^–2k^9\frac{2\widehat{i} + 2\widehat{j}–2\widehat{k}}{9}

B

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

C

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

D

None of these

Answer

2i^+2j^–2k^9\frac{2\widehat{i} + 2\widehat{j}–2\widehat{k}}{9}

Explanation

Solution

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