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Question

Let $\overrightarrow a = 4\widehat i + 3\widehat j$ and $\overrightarrow b = 3\widehat i - 4\widehat j + 5\widehat k$. If $\overrightarrow c $ is a vector such that $\overrightarrow c .\left( {\overrightarrow a \times \overrightarrow b } \right) + 25 = 0,\overrightarrow c \,.(\widehat i + \widehat j + \widehat k) = 4$, and projection of $\overrightarrow c $ on $\overrightarrow a $ is 1, then the projection of $\overrightarrow c $ on $\overrightarrow b $ equals :

$\frac{3}{\sqrt2}$
$\frac{1}{\sqrt2}$
$\frac{1}{5}$
$\frac{5}{\sqrt2}$

Solution

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