Question

What is the angle between i+j+k and 2i+2j+2K?
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Answer 1

Hi,

Here is your answer

Given:

1i+1j+1k

2i+2j+2k

To Find:

Angle between the vectors

Solution

First find the dot product of the two vectors.

$\vec{a}.\vec{b}=(\vec{i}+\vec{j}+\vec{k}).(2\vec{i}+2\vec{j}+2\vec{k})$

$\vec{a}.\vec{b}=2\times1+2\times1+2\times1=6$

Now find the magnitude of each vector

$|\vec{a}|=\sqrt{1+1+1} =\sqrt{3}$

$|\vec{b}|=\sqrt{2^{2} +2^{2} +2^{2} } =\sqrt{12}=2\sqrt{3}$

Now

$CosA=\frac{\vec{a}.\vec{b}}{|\vec{a}||\vec{b}|}$

$CosA=\frac{6}{\sqrt{3}\times2\sqrt{3} }$

$CosA=\frac{3}{3} =1$

$CosA=Cos0$

Hence angle between the vectors=0.

Hope this helps you.