Question

the angle between two vectors -2icap+3jcap+kcap and icap+2jcap-4kcap is​

Answer 1

Explanation:

We have,

(Let the given Vectors be A and B respectively.)

$\sf{A=-2i+3j+k}$

And, $\sf{B=i+2j-4k}$

To find,

Angle between both Vectors, $\sf{\Theta =?}$

Now,

$\sf{A.B=|A|\times{|B|}\cos(\Theta)}$

$\implies{\sf{(-2i+3j+k).(i+2j-4k)=\sqrt{(-2)^{2}+(3)^{2}+(1)^{2}}\times{\sqrt{(1)^{2}+(2)^{2}+(-4)^{2}}}\times{\cos(\Theta)}}}$

$\implies{\sf{-2+6-4=\sqrt{4+9+1}\times{\sqrt{1+4+16}}\times{\cos(\Theta)}}}$

$\implies{\sf{0=\sqrt{14}\times{\sqrt{21}}\times{\cos(\Theta)}}}$

$\implies{\sf{0=\cos(\Theta)}}$

Therefore,

$\implies{\boxed{\sf{\Theta=90°}}}$

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