A vector vec{P} makes angles alpha, beta, and | 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: $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$.Using the trigonometric identity $\s

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(C) For any vector,the direction cosines satisfy the relation: $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$.Using the trigonometric identity $\sin^2 	heta = 1 - \cos^2 	heta$,we can rewrite the expression as:$(1 - \sin^2 \alpha) + (1 - \sin^2 \beta) + (1 - \sin^2 \gamma) = 1$.Rearranging the terms:$3 - (\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma) = 1$.Therefore,$\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = 3 - 1 = 2$.

$A$ vector $\vec{P}$ 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

Calculate the shortest wavelength in the hydrogen spectrum emission of the Lyman series $(R_H = 109677 \text{ cm}^{-1})$.

The value of a unit vector in the direction of vector $\vec A = 5\hat i - 12\hat j$ is:

Define scalar and vector physical quantities with their examples.

The cosine values of the angles made by the vector $\vec{A} = \hat{i} + \hat{j} + \hat{k}$ with the $X$,$Y$,and $Z$ axes respectively are:

The magnitude of the vector $|2\hat{i} - \hat{j} - 5\hat{k}|$ is .....

Vedclass Test Series

Exam Paper Generator

Online Exam Module