Question

If i , j, and k represent unit vectors along the x , y and z - axis respectively , then the angle theta between the vectors i + j +k and i + j is equal to

Answer 1

The answer is provided below:-

Answer 2

Answer:

The angle between the vectors is $\theta=cos^{-1}\dfrac{2}{\sqrt{6}}$.

Explanation:

Given that,

Let us consider the vector A= i+j+k and vector B = i+j.

If i , j, and k represent unit vectors along the x , y and z - axis respectively.

The angle between the vectors is

$cos\theta = \dfrac{\vec{A}\cdot\vec{B}}{|A|\cdot|B|}$

$cos\theta=\dfrac{(i+j+k)\cdot(i+j)}{\sqrt{3}\cdot\sqrt{2}}$

$cos\theta=\dfrac{2}{\sqrt{6}}$

$\theta=cos^{-1}\dfrac{2}{\sqrt{6}}$

Hence, The angle between the vectors is $\theta=cos^{-1}\dfrac{2}{\sqrt{6}}$.