Question

Find the projection of vector a=2i-j+k along b=i+2j+2k

Answer 1

a.b=2-2+2=2. |b|=√1+4+4=√9=3. projection= 2/3

Answer 2

The projection of vector A on B is $\dfrac{2}{3}$.

Explanation:

Given that,

Vector $A=2i-j+k$

Vector $B=i+2j+2k$

We need to find the projection of vector A on B. Let it is given by c. It can be calculated as :

$c=\dfrac{A{\cdot}B}{|b|}$

$c=\dfrac{2i-j+k {\cdot}i+2j+2k}{\sqrt{1^2+2^2+2^2}}$

$c=\dfrac{2-2+2}{3}$

$c=\dfrac{2}{3}$

So, the projection of vector A on B is $\dfrac{2}{3}$. Hence, this is the required solution.

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