If a vector overrightarrow{P} makes angles al | vedclass

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

Question

(C) For any vector,the direction cosines satisfy the relation $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$.We know the trigonometric identity $\

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(C) For any vector,the direction cosines satisfy the relation $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$.We know the trigonometric identity $\sin^2 	heta = 1 - \cos^2 	heta$.Substituting this into the expression:$\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = (1 - \cos^2 \alpha) + (1 - \cos^2 \beta) + (1 - \cos^2 \gamma)$$= 3 - (\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma)$$= 3 - 1$$= 2$

If a vector $\overrightarrow{P}$ makes angles $\alpha, \beta,$ and $\gamma$ with the $X, Y,$ and $Z$ axes respectively,then $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = $

Similar Questions

If $A$ and $B$ are two vectors such that $|A + B| = 2|A - B|$,the angle between vectors $A$ and $B$ is:

The angle made by the vector $(\hat{i} + \hat{j})$ with the $x$-axis and $y$-axis is:

$0.4\hat i + 0.8\hat j + c\hat k$ represents a unit vector when $c$ is

$A$ force,$\vec{F}=(4 \hat{i}+3 \hat{j}-5 \hat{k}) \text{ N}$,is acting on a body. If the horizontal direction is taken along the $\hat{i} + \hat{j}$ direction,find the angle $\theta$ that the force makes with this horizontal direction.

If $|\vec{v}_1 + \vec{v}_2| = |\vec{v}_1 - \vec{v}_2|$ and $\vec{v}_1$ and $\vec{v}_2$ are finite,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module