The angle between two vectors vec{a} = hat{i} | vedclass

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

Question

(B) The angle $	heta$ between two vectors $\vec{a}$ and $\vec{b}$ is given by the formula: $\cos 	heta = \frac{\vec{a} \cdot \vec{b}}{|\vec{a}| |\ve

Vedclass · Accepted Answer

$\cos^{-1} \left(-\frac{1}{3}\right)$

Vedclass · Answer

(B) The angle $	heta$ between two vectors $\vec{a}$ and $\vec{b}$ is given by the formula: $\cos 	heta = \frac{\vec{a} \cdot \vec{b}}{|\vec{a}| |\vec{b}|}$.Given $\vec{a} = \hat{i} - \hat{j} + \hat{k}$ and $\vec{b} = \hat{i} + \hat{j} - \hat{k}$.First,calculate the dot product: $\vec{a} \cdot \vec{b} = (1)(1) + (-1)(1) + (1)(-1) = 1 - 1 - 1 = -1$.Next,calculate the magnitudes: $|\vec{a}| = \sqrt{1^2 + (-1)^2 + 1^2} = \sqrt{3}$ and $|\vec{b}| = \sqrt{1^2 + 1^2 + (-1)^2} = \sqrt{3}$.Now,substitute these values into the formula: $\cos 	heta = \frac{-1}{\sqrt{3} \cdot \sqrt{3}} = \frac{-1}{3}$.Therefore,$	heta = \cos^{-1} \left(-\frac{1}{3}ight)$.

The angle between two vectors $\vec{a} = \hat{i} - \hat{j} + \hat{k}$ and $\vec{b} = \hat{i} + \hat{j} - \hat{k}$ is . . . . . . .

Similar Questions

If $\overline{a}, \overline{b}, \overline{c}$ are unit vectors and $\theta$ is the angle between $\overline{a}$ and $\overline{c}$ and $\overline{a}+2 \overline{b}+2 \overline{c}=\overline{0}$,then $|\overline{a} \times \overline{c}|=$

If $\vec{a}$ is a unit vector and $(\vec{x}-\vec{a}) \cdot (\vec{x}+\vec{a}) = 8$,then $|\vec{x}| = $ . . . . . . .

If the moduli of the vectors $a, b, c$ are $3, 4, 5$ respectively and $a$ and $b + c$,$b$ and $c + a$,$c$ and $a + b$ are mutually perpendicular,then the modulus of $a + b + c$ is

The position vectors of the vertices of $\triangle ABC$ are $4\hat{i} - 2\hat{j}$,$\hat{i} + 4\hat{j} - 3\hat{k}$,and $-\hat{i} + 5\hat{j} + \hat{k}$ respectively. Then,$m \angle ABC = $

The work done by the force $F = 2i - 3j + 2k$ in displacing a particle from the point $(3, 4, 5)$ to the point $(1, 2, 3)$ is ............ $unit$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module