The component of hati in the direction of the vector hati + hatj +2 hatk is

Question

The component of hati in the direction of the vector hati + hatj +2 hatk is (A) √6 (B) 6 (C) 6√6 (D) (√6/6)

Tardigrade Admin · Accepted Answer

Unit vector along hati + hatj +2 hatk is ( hati + hatj +2 hatk/√6) Hence, the component of hati along the given vector, = Projection of hati on ( hati + hatj +2 hatk/√6) = hati⋅(( hati + hatj +2 hatk)/√6) = (1/√6) = (√6/6)

Q. The component of $\hat{i}$ in the direction of the vector $\hat{i} + \hat{j} + 2 \hat{k}$ is

$6$

$6$

$66$

$\frac{6}{6}$

Unit vector along $\hat{i} + \hat{j} + 2 \hat{k}$ is $\frac{i ^ + j ^ + 2 k ^}{6}$
Hence, the component of $\hat{i}$ along the given vector,
$=$ Projection of $\hat{i}$ on $\frac{i ^ + j ^ + 2 k ^}{6}$
$= \hat{i} \cdot \frac{( i ^ + j ^ + 2 k ^ )}{6} = \frac{1}{6}$
$= \frac{6}{6}$

Q. The component of i^ in the direction of the vector i^+j^​+2k^ is

6​

6

66​

66​​

Unit vector along i^+j^​+2k^ is 6​i^+j^​+2k^​ Hence, the component of i^ along the given vector, = Projection of i^ on 6​i^+j^​+2k^​ =i^⋅6​(i^+j^​+2k^)​=6​1​ =66​​

Q. The component of $\hat{i}$ in the direction of the vector $\hat{i} + \hat{j} + 2 \hat{k}$ is

$6$

$6$

$66$

$\frac{6}{6}$

Unit vector along $\hat{i} + \hat{j} + 2 \hat{k}$ is $\frac{i ^ + j ^ + 2 k ^}{6}$
Hence, the component of $\hat{i}$ along the given vector,
$=$ Projection of $\hat{i}$ on $\frac{i ^ + j ^ + 2 k ^}{6}$
$= \hat{i} \cdot \frac{( i ^ + j ^ + 2 k ^ )}{6} = \frac{1}{6}$
$= \frac{6}{6}$