If a and b are unit vectors such that a+b is | vedclass

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

Question

(D) Given that $a$ and $b$ are unit vectors,we have $|a| = 1$ and $|b| = 1$. Also,$a+b$ is a unit vector,so $|a+b| = 1$. Squaring both sides,we get $|

Vedclass · Accepted Answer

$120$

Vedclass · Answer

(D) Given that $a$ and $b$ are unit vectors,we have $|a| = 1$ and $|b| = 1$. Also,$a+b$ is a unit vector,so $|a+b| = 1$. Squaring both sides,we get $|a+b|^2 = 1^2 = 1$. Using the property $|a+b|^2 = |a|^2 + |b|^2 + 2(a \cdot b)$,we have: $1^2 + 1^2 + 2(a \cdot b) = 1$ $1 + 1 + 2(a \cdot b) = 1$ $2 + 2(a \cdot b) = 1$ $2(a \cdot b) = -1$ $a \cdot b = -\frac{1}{2}$. Since $a \cdot b = |a||b| \cos 	heta$,where $	heta$ is the angle between $a$ and $b$: $(1)(1) \cos 	heta = -\frac{1}{2}$ $\cos 	heta = -\frac{1}{2}$. Therefore,$	heta = 120^{\circ}$. Hence,option $D$ is correct.

If $a$ and $b$ are unit vectors such that $a+b$ is also a unit vector,then the angle between $a$ and $b$ is . . . . . . (in $^{\circ}$)

Similar Questions

Let $A=(3,4,0), B=(4,4,4), C=(-6,2,3)$ and $D=(1,1,2)$. If $\theta$ is the acute angle between the lines $AB$ and $CD$, then $\cos \theta=$

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

Find the distance of the point $P(-\hat{i} + 2\hat{j} + 6\hat{k})$ from the line passing through the point $A(2\hat{i} + 3\hat{j} - 4\hat{k})$ and parallel to the vector $\vec{b} = 6\hat{i} + 3\hat{j} - 4\hat{k}$.

Let $a, b, c$ be three vectors such that $a \neq 0$,$a \times b = 2a \times c$,$|a| = |c| = 1$,$|b| = 4$,and $|b \times c| = \sqrt{15}$. If $b - 2c = \lambda a$,then $\lambda$ equals:

The angle between the vectors $(2i + 6j + 3k)$ and $(12i - 4j + 3k)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module