Question

find the angle between the vectors A vector=icap+jcap+kcap and B vector=-2icap-2jcap-2kcap​

Answer 1

Answer:

The angle between the vectors $A=i+j+k$ and vector $B=-2i-2j-2k$ is $\alpha =0$

Explanation:

A vector is a physical quantity that has both magnitude and direction

To find the angle between two vectors we can use the dot product if A and B are two vectors inclined to an angle $\alpha$

so the dot product is given by the formula

$A.B=/A//B/cos\alpha$

from the question, we have two vectors

$A=i+j+k$ and $B=-2i-2j-2k$

the angle between these two vectors is

$cos\alpha =\frac{A.B}{/A//B/}$

the dot product of A and B is $A.B=(-2*1)+(-2*1)+(-2*1)=-6$

the magnitude of vector A is $/A/=\sqrt{1^{2} +1^{2} +1^{2} } =\sqrt{3}$

that of vector B is $/B/=\sqrt{2^{2} +2^{2} +2^{2} }=\sqrt{12}$

therefore the angle is $\alpha =cos^{-1} (\frac{-6}{\sqrt{3}*\sqrt{12} } )=0$

that is the two vectors are parallel vectors