Let the vectors overline{a}, overline{b}, ove | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given: $|\overline{a}|=2, |\overline{b}|=4, |\overline{c}|=4$.According to the condition,the projection of $\overline{b}$ on $\overline{a}$ is equ

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(B) Given: $|\overline{a}|=2, |\overline{b}|=4, |\overline{c}|=4$.According to the condition,the projection of $\overline{b}$ on $\overline{a}$ is equal to the projection of $\overline{c}$ on $\overline{a}$.$\frac{\overline{b} \cdot \overline{a}}{|\overline{a}|} = \frac{\overline{c} \cdot \overline{a}}{|\overline{a}|}$$\implies \overline{b} \cdot \overline{a} = \overline{c} \cdot \overline{a}$$\implies (\overline{b} - \overline{c}) \cdot \overline{a} = 0$ ... $(i)$Also,$\overline{b}$ is perpendicular to $\overline{c}$,so $\overline{b} \cdot \overline{c} = 0$.Now,consider $|\overline{a} + \overline{b} - \overline{c}|^2 = |\overline{a}|^2 + |\overline{b} - \overline{c}|^2 + 2\overline{a} \cdot (\overline{b} - \overline{c})$.From $(i)$,$\overline{a} \cdot (\overline{b} - \overline{c}) = 0$.So,$|\overline{a} + \overline{b} - \overline{c}|^2 = |\overline{a}|^2 + |\overline{b}|^2 + |\overline{c}|^2 - 2(\overline{b} \cdot \overline{c})$.Since $\overline{b} \cdot \overline{c} = 0$,we have:$|\overline{a} + \overline{b} - \overline{c}|^2 = (2)^2 + (4)^2 + (4)^2 - 0 = 4 + 16 + 16 = 36$.Therefore,$|\overline{a} + \overline{b} - \overline{c}| = \sqrt{36} = 6$.

Similar Questions

If $\bar{a}$ and $\bar{b}$ are mutually perpendicular unit vectors,then $(3\bar{a}+2\bar{b}) \cdot (5\bar{a}-6\bar{b}) = $

Let $\bar{a}, \bar{b}$ and $\bar{c}$ be vectors of magnitude $2, 3$ and $4$ respectively. If $\bar{a}$ is perpendicular to $(\bar{b}+\bar{c})$,$\bar{b}$ is perpendicular to $(\bar{c}+\bar{a})$ and $\bar{c}$ is perpendicular to $(\bar{a}+\bar{b})$,then the magnitude of $\bar{a}+\bar{b}+\bar{c}$ is

If $\vec{a}$ and $\vec{b}$ are unit vectors such that the vector $\vec{a} + 3\vec{b}$ is perpendicular to $7\vec{a} - 5\vec{b}$,then find the angle between $\vec{a}$ and $\vec{b}$.

The value of $\lambda$ for which the vectors $2\lambda \hat{i} + \hat{j} - \hat{k}$ and $2\hat{j} + \hat{k}$ are perpendicular is:

Let $a, b$ and $c$ be three non-coplanar vectors. The vector equation of a line which passes through the point of intersection of two lines,one joining the points $a+2b-5c$ and $-a-2b-3c$,and the other joining the points $-4c$ and $6a-4b+4c$,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module