Question

The components of a vector a along and perpendicular to the non-zero vector b are respectively

• A. $\frac{\mathbf{a}.\mathbf{b}}{|\mathbf{a}|},\frac{|\mathbf{a} \times \mathbf{b}|}{|\mathbf{a}|}$
• B. $\frac{\mathbf{a}.\mathbf{b}}{|\mathbf{b}|},\frac{|\mathbf{a} \times \mathbf{b}|}{|\mathbf{b}|}$
• C. $\frac{\mathbf{a}.\mathbf{b}}{|\mathbf{a}|},\frac{\mathbf{a}.\mathbf{b}}{|\mathbf{a}|}$
• D. $\frac{|\mathbf{a} \times \mathbf{b}|}{|\mathbf{a}|},\frac{|\mathbf{a} \times \mathbf{b}|}{|\mathbf{b}|}$

Answer 1

Answer: (B)

$\frac{\mathbf{a}.\mathbf{b}}{|\mathbf{b}|},\frac{|\mathbf{a} \times \mathbf{b}|}{|\mathbf{b}|}$

Answer 2

Component of $\mathbf{a}$ along $\mathbf{b} = a\cos\theta = \frac{|\mathbf{a}.\mathbf{b}|}{|\mathbf{b}|}$

Similarly component of $\mathbf{a}$ perpendicular to $\mathbf{b}$

$= a\sin\theta = \frac{|\mathbf{a} \times \mathbf{b}|}{|\mathbf{b}|}.$