If the vector vec{a} = hat{i} + hat{j} + hat{ | vedclass

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

Question

(D) Let $\vec{v} = \hat{i} + \hat{j} + \hat{k}$. The magnitude is $|\vec{v}| = \sqrt{1^2 + 1^2 + 1^2} = \sqrt{3}$.The angle $\alpha$ between $\vec{v}$

Vedclass · Accepted Answer

$\alpha = \beta = \gamma$

Vedclass · Answer

(D) Let $\vec{v} = \hat{i} + \hat{j} + \hat{k}$. The magnitude is $|\vec{v}| = \sqrt{1^2 + 1^2 + 1^2} = \sqrt{3}$.The angle $\alpha$ between $\vec{v}$ and $\hat{i}$ is given by $\cos \alpha = \frac{\vec{v} \cdot \hat{i}}{|\vec{v}| |\hat{i}|} = \frac{(\hat{i} + \hat{j} + \hat{k}) \cdot \hat{i}}{\sqrt{3} \cdot 1} = \frac{1}{\sqrt{3}}$. Thus,$\alpha = \cos^{-1}(\frac{1}{\sqrt{3}})$.The angle $\beta$ between $\vec{v}$ and $\hat{j}$ is given by $\cos \beta = \frac{\vec{v} \cdot \hat{j}}{|\vec{v}| |\hat{j}|} = \frac{(\hat{i} + \hat{j} + \hat{k}) \cdot \hat{j}}{\sqrt{3} \cdot 1} = \frac{1}{\sqrt{3}}$. Thus,$\beta = \cos^{-1}(\frac{1}{\sqrt{3}})$.The angle $\gamma$ between $\vec{v}$ and $\hat{k}$ is given by $\cos \gamma = \frac{\vec{v} \cdot \hat{k}}{|\vec{v}| |\hat{k}|} = \frac{(\hat{i} + \hat{j} + \hat{k}) \cdot \hat{k}}{\sqrt{3} \cdot 1} = \frac{1}{\sqrt{3}}$. Thus,$\gamma = \cos^{-1}(\frac{1}{\sqrt{3}})$.Therefore,$\alpha = \beta = \gamma$.

If the vector $\vec{a} = \hat{i} + \hat{j} + \hat{k}$ makes angles $\alpha, \beta, \gamma$ with vectors $\hat{i}, \hat{j}, \hat{k}$ respectively,then:

Similar Questions

Let $\vec{a}=x \hat{i}+y \hat{j}+z \hat{k}$ and $x=2 y$. If $|\vec{a}|=5 \sqrt{2}$ and $\vec{a}$ makes an angle of $135^{\circ}$ with the $z$-axis,then $\vec{a}=$

Two vectors $u$ and $v$ are parallel if and only if

Classify the following measure as a scalar or a vector:
$20 \text{ m/s}$ towards north

If the orthocentre of the triangle whose vertices are $2 \hat{i}+3 \hat{j}+5 \hat{k}$,$5 \hat{i}+2 \hat{j}+3 \hat{k}$,and $3 \hat{i}+5 \hat{j}+2 \hat{k}$ is $x \hat{i}+y \hat{j}+z \hat{k}$,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module