1. Tardigrade
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  4. Assertion: The projection of the vector a =2 hat i +3 hat j +2 hat k on the vector vec b = hat i +2 hat j + hat k is (5/3) √6. Reason The projection of vector a on vector b is (1/| a |) (a.b).

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Q. Assertion : The projection of the vector $a =2 \hat{ i }+3 \hat{ j }+2 \hat{ k }$ on the vector $\vec{ b }=\hat{ i }+2 \hat{ j }+\hat{ k }$ is $\frac{5}{3} \sqrt{6}$.
Reason The projection of vector a on vector $b$ is $\frac{1}{| a |}$ (a.b).

Vector Algebra

Solution:

The projection of vector a on the vector $b$ is given by
$\frac{(a \cdot b)}{|b|}=\frac{(2 \times 1+3 \times 2+2 \times 1)}{\sqrt{(1)^{2}+(2)^{2}+(1)^{2}}}=\frac{10}{\sqrt{6}}=\frac{5}{3} \sqrt{6}$