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 $\hat{a}$ and $\hat{b}$ be unit vectors. If $\vec{c}$ is a vector such that the angle between $\hat{a}$ and $\vec{c}$ is $\frac{\pi}{12}$,and $\hat{b} = \vec{c} + 2(\vec{c} \times \hat{a})$,then $|6\vec{c}|^{2}$ is equal to

If $\vec{a}, \vec{b}, \vec{c}$ and $\vec{d}$ are unit vectors such that $(\vec{a} \times \vec{b}) \cdot (\vec{c} \times \vec{d}) = 1$ and $\vec{a} \cdot \vec{c} = \frac{1}{2}$,then :-

If $a, b$ and $c$ are unit vectors such that $a+b+c=0$,then $a \cdot b+b \cdot c+c \cdot a$ is equal to

$A$ unit vector in the $xy$-plane that makes an angle of $45^{\circ}$ with the vector $(i + j)$ and an angle of $60^{\circ}$ with the vector $(3i - 4j)$ is:

$\bar{a}, \bar{b}, \bar{c}$ are unit vectors. If $\bar{a}, \bar{b}$ are perpendicular vectors,$(\bar{a}-\bar{c}) \cdot(\bar{b}+\bar{c})=0$ and $\bar{c}=l \bar{a}+m \bar{b}+n(\bar{a} \times \bar{b})$ ($l, m, n$ are scalars),then $n^2=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module