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Chiral Centres and Chirality

If a=4i+6j ...

Question

If $a = 4 i + 6 j$ and $b = 3 j + 4 k,$ findthe projection of a along b.

A

\frac{18}{25} (- 3 j - 4 k) .

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B

\frac{18}{25} (3 j + 4 k) .

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C

\frac{18}{25} (4 i + 6 j) .

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D

\frac{18}{25} (- 4 i - 6 j) .

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Solution

The correct option is B $\frac{18}{25} (3 j + 4 k) .$
Projection of $a$ along $b$ is $\frac{a . b}{| b |}$
$= \frac{4.0 + 6.3 + 0.4}{5} = \frac{18}{5} .$
Hence the vector determined by this projection is
$\frac{18}{5}^b = \frac{18}{5} (\frac{3 j + 4 k}{5}) = \frac{18}{25} (3 j + 4 k) .$

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