Angle between two vectors - 2hat{i} + 3hat{j} + hat{k} and hat{i} + 2hat{j} - 4hat{k} is ......

English

Gujarati

Hindi

3-1.Vectors

medium

The angle between two vectors $ - 2\hat i + 3\hat j + \hat k$ and $\hat i + 2\hat j - 4\hat k$ is ....... $^o$

A

$0$

B

$90$

C

$180$

D

None of the above

Solution

(b) $\cos \theta = \frac{{\vec A.\vec B}}{{|\vec A||\vec B|}} = \frac{{ – 2 + 6 – 4}}{{\sqrt {14} \sqrt {21} }} = 0$

$\therefore \theta = 90^\circ $

Standard 11

Physics

Share

Similar Questions

Find the angle between two vectors $\vec A = 2\hat i + \hat j – \hat k$ and $\vec B = \hat i – \hat k$ ……. $^o$

medium

The values of $x$ and $y$ for which vectors $\vec A = \left( {6\hat i + x\hat j – 2\hat k} \right)$ and $\vec B = \left( {5\hat i – 6\hat j – y\hat k} \right)$ may be parallel are

medium

If two vectors $\vec{P}=\hat{i}+2 m \hat{j}+m \hat{k}$ and $\vec{Q}=4 \hat{i}-2 \hat{j}+ mk$ are perpendicular to each other. Then, the value of $m$ will be :

medium

(JEE MAIN-2023)

For three vectors $\vec{A}=(-x \hat{i}-6 \hat{j}-2 \hat{k})$, $\vec{B}=(-\hat{i}+4 \hat{j}+3 \hat{k})$ and $\vec{C}=(-8 \hat{i}-\hat{j}+3 \hat{k})$, if $\overrightarrow{\mathrm{A}} \cdot(\overrightarrow{\mathrm{B}} \times \overrightarrow{\mathrm{C}})=0$, them value of $\mathrm{x}$ is. . . . . ..

hard

(JEE MAIN-2024)

The vector sum of two forces is perpendicular to their vector differences. In that case, the forces

medium

(AIIMS-2012)