What is the angle between $< 1, - 2, 7 >$ $<1 , -2 , 7 >$ and $< 7, - 2, 2 >$ $< 7 , -2 , 2 >$ ?

Question

1586 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-10T06:27:08

The angle is $=63.2º$

The angle between two vectors is given by the dot product.

$vecu.vecv=∥vecu∥*∥vecv∥ costheta$
$theta$ is the angle between the two vectors

Here $vecu.vecv=〈1,-2,7〉.〈7,-2,2〉=7+4+14=25$
The modulus of the vectors are :

$∥〈1,-2,7〉∥ = sqrt(1+4+49) = sqrt(54)$

$∥〈7,-2,2〉∥= sqrt(49+4+4)= sqrt57$

#costheta=vecu.vecv/(∥vecu∥*∥vecv∥)=25/(sqrt54*sqrt57)=0.45#

$theta=63.2º$

What is the angle between <1 , -2 , 7 > <1,−2,7><1 , -2 , 7 > and < 7 , -2 , 2 > <7,−2,2> < 7 , -2 , 2 > ?