If overline{a} and overline{b} are two unit v | vedclass

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

Question

(B) Let $	heta$ be the angle between $\overline{a}$ and $\overline{b}$.Since $\overline{a}$ and $\overline{b}$ are unit vectors,$|\overline{a}| = 1$

Vedclass · Accepted Answer

$\frac{\pi}{3}$

Vedclass · Answer

(B) Let $	heta$ be the angle between $\overline{a}$ and $\overline{b}$.Since $\overline{a}$ and $\overline{b}$ are unit vectors,$|\overline{a}| = 1$ and $|\overline{b}| = 1$.Given that $\overline{c} = \overline{a} + 2\overline{b}$ and $\overline{d} = 5\overline{a} - 4\overline{b}$ are perpendicular,their dot product is zero:$\overline{c} \cdot \overline{d} = 0$$(\overline{a} + 2\overline{b}) \cdot (5\overline{a} - 4\overline{b}) = 0$$5(\overline{a} \cdot \overline{a}) - 4(\overline{a} \cdot \overline{b}) + 10(\overline{b} \cdot \overline{a}) - 8(\overline{b} \cdot \overline{b}) = 0$$5|\overline{a}|^2 + 6(\overline{a} \cdot \overline{b}) - 8|\overline{b}|^2 = 0$Since $|\overline{a}| = 1$ and $|\overline{b}| = 1$,and $\overline{a} \cdot \overline{b} = |\overline{a}||\overline{b}| \cos 	heta = \cos 	heta$:$5(1) + 6 \cos 	heta - 8(1) = 0$$6 \cos 	heta - 3 = 0$$6 \cos 	heta = 3$$\cos 	heta = \frac{3}{6} = \frac{1}{2}$$	heta = \cos^{-1}\left(\frac{1}{2}ight) = \frac{\pi}{3}$.

If $\overline{a}$ and $\overline{b}$ are two unit vectors such that $\overline{a}+2\overline{b}$ and $5\overline{a}-4\overline{b}$ are perpendicular to each other,then the angle between $\overline{a}$ and $\overline{b}$ is

Similar Questions

Let $a = i + 2j + k$,$b = i - j + k$,$c = i + j - k$. $A$ vector in the plane of $a$ and $b$ has projection $\frac{1}{\sqrt{3}}$ on $c$. Then,one such vector is

If $\vec{p}, \vec{q}, \text{ and } \vec{r}$ are three mutually perpendicular vectors of the same magnitude,find the angle between $\vec{p}$ and $\vec{p} + \vec{q} + \vec{r}$.

If $\bar{a}=\hat{i}+2 \hat{j}+\hat{k}$,$\bar{b}=\hat{i}-\hat{j}+\hat{k}$,and $\bar{c}=\hat{i}+\hat{j}-\hat{k}$,then a vector in the plane of $\bar{a}$ and $\bar{b}$,whose projection on $\bar{c}$ is $\frac{1}{\sqrt{3}}$,is

If $a\hat{i} + 6\hat{j} - \hat{k}$ and $7\hat{i} - 3\hat{j} + 17\hat{k}$ are perpendicular vectors,then what is the value of $a$?

$A$ particle is acted upon by constant forces $4\hat{i} + \hat{j} - 3\hat{k}$ and $3\hat{i} + \hat{j} - \hat{k}$. The displacement of the particle from the point $\hat{i} + 2\hat{j} + 3\hat{k}$ to the point $5\hat{i} + 4\hat{j} + \hat{k}$ is given. Find the total work done by the forces in units.

Vedclass Test Series

Exam Paper Generator

Online Exam Module