If projection of 2 hat{i}+4 hat{j}-2 hat{k} on hat{i}+2 hat{j}+α hat{k} is zero. Then, value of α

English

Gujarati

Hindi

3-1.Vectors

hard

If the projection of $2 \hat{i}+4 \hat{j}-2 \hat{k}$ on $\hat{i}+2 \hat{j}+\alpha \hat{k}$ is zero. Then, the value of $\alpha$ will be.

A

$2$

B

$3$

C

$5$

D

$4$

(JEE MAIN-2022)

Solution

$\overrightarrow{ a } \cdot \overrightarrow{ b }=0$

$\therefore \overrightarrow{ a } \cdot \overrightarrow{ b }=0$

$\therefore 2 \times 1+4 \times 2-2 \times \alpha=0$

$\therefore \alpha=5$

Standard 11

Physics

Share

Similar Questions

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

medium

(AIIMS-2012)

If $F _1$ and $F _2$ are two vectors of equal magnitudes $F$ such that $\left| F _1 \cdot F _2\right|=\left| F _1 \times F _2\right|$, then $\left| F _1+ F _2\right|$ equals to

medium

Consider a vector $\overrightarrow F = 4\hat i – 3\hat j.$ Another vector that is perpendicular to $\overrightarrow F $ is

easy

If for two vector $\overrightarrow A $ and $\overrightarrow B $, sum $(\overrightarrow A + \overrightarrow B )$ is perpendicular to the difference $(\overrightarrow A – \overrightarrow B )$. The ratio of their magnitude is

hard

Unit vector perpendicular to vector $A =-3 \hat{ i }-2 \hat{ j }-3 \hat{ k }$ and $B =2 \hat{ i }+4 \hat{ j }+6 \hat{ k }$ both is

medium