Question

Statement I The projection of the vector $a =2 \hat{ i }+3 \hat{ j }+2 \hat{ k }$ on the vector $b =\hat{ i }+2 \hat{ j }+\hat{ k }$ is $\frac{5}{3} \sqrt{6}$
Statement II The projection of vector a on vector $b$ is $\frac{1}{| a |}( a \cdot b )$

• A. Statement I is true; statement II is true; statement II is a correct explanation for statement I
• B. Statement I is true; statement II is true; statement II is not a correct explanation for statement I
• C. Statement I is true; statement II is false
• D. Statement I is false; statement II is true

Answer 1

Answer: (C)

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