If alpha, beta and gamma are the angles made | vedclass

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

Question

(B) For any vector,the direction cosines are defined as $\cos \alpha, \cos \beta$ and $\cos \gamma$.We know the fundamental identity for direction cos

Vedclass · Accepted Answer

$1 + \cos ^2 \gamma$

Vedclass · Answer

(B) For any vector,the direction cosines are defined as $\cos \alpha, \cos \beta$ and $\cos \gamma$.We know the fundamental identity for direction cosines is $\cos ^2 \alpha + \cos ^2 \beta + \cos ^2 \gamma = 1$.Using the trigonometric identity $\sin ^2 	heta = 1 - \cos ^2 	heta$,we can rewrite the expression as:$(1 - \sin ^2 \alpha) + (1 - \sin ^2 \beta) + (1 - \sin ^2 \gamma) = 1$.$3 - (\sin ^2 \alpha + \sin ^2 \beta + \sin ^2 \gamma) = 1$.$\sin ^2 \alpha + \sin ^2 \beta + \sin ^2 \gamma = 2$.Therefore,$\sin ^2 \alpha + \sin ^2 \beta = 2 - \sin ^2 \gamma$.Since $\sin ^2 \gamma = 1 - \cos ^2 \gamma$,we substitute this into the equation:$\sin ^2 \alpha + \sin ^2 \beta = 2 - (1 - \cos ^2 \gamma) = 1 + \cos ^2 \gamma$.

If $\alpha, \beta$ and $\gamma$ are the angles made by a vector with $x, y$ and $z$ axes respectively,then $\sin ^2 \alpha + \sin ^2 \beta =$

Similar Questions

Explain the null vector. Explain the physical significance of the null vector.

$\vec{A}$ and $\vec{B}$ are two non-zero vectors inclined at an angle $\theta$. $\hat{a}$ and $\hat{b}$ are unit vectors along $\vec{A}$ and $\vec{B}$ respectively. The component of $\vec{A}$ in the direction of $\vec{B}$ is

When $\vec A \cdot \vec B = - |A||B|$,then

$A$ vector $\vec{A}$ is rotated by a small angle $\Delta \theta$ radian $(\Delta \theta \ll 1)$ to get a new vector $\vec{B}$. In that case,$|\vec{B} - \vec{A}|$ is

Given that $\overrightarrow A + \overrightarrow B + \overrightarrow C = 0$. Out of three vectors,two are equal in magnitude and the magnitude of the third vector is $\sqrt{2}$ times that of either of the two having equal magnitude. Then the angles between the vectors are given by:

Vedclass Test Series

Exam Paper Generator

Online Exam Module