Question

find the projection of b +c vector on a vector where a =2i-2j+k,b=i+2j-2k and c=2i-j+4k​

Answer 1

Given:

$a \: = 2 \hat i - 2 \hat j + \: \hat k$

$b\: = \hat i + 2 \hat j - 2 \: \hat k</p><p>$

$c= 2 \hat i - \hat j + 4\hat k</p><p>$

To find :

Projection of b+c on a

Solution:

$b + c =( \hat i + 2\hat j - 2 \hat k) + (2\hat i - \hat j + 4\hat k)$

$b + c = 3\hat i + \hat j + 2 \hat k \:$

So,

Formula of Projection of b+c on a:

$= \: \bf \: \frac{(b + c) \cdot \: a}{ |a| }$

Here |a| is the magnitude of vector a :

So,

$|a| = \sqrt{ {2}^{2} + {2}^{2} + {1}^{2} } = \sqrt{9} = 3$

So,

Putting the values of (b+c), a and |a| in the formula of projection.

The projection of (b+c) on a =

$= \: \bf \: \frac{(3 \hat i + \hat j + 2\hat k) \cdot \: (2 \hat i - 2 \hat j + \hat k)}{ 3 }$

$= \: \bf \: \frac{(6 - 2 + 2)}{ 3 } = \frac{6}{3} = 2$

So, the projection of (b+c) on a = 2