What is the angle between < 6 , 1 , -4 > and < 2 , -3 , 2 > ?

1 Answer
Jan 28, 2016

88^@

Explanation:

To find the angle between 2 vectors use the following formula :

costheta =( veca.vecb)/((|veca| xx |vecb|)

where a and b represent the 2 vectors and
theta color(black)(" the angle between them")

let veca = (6,1,-4) , vecb = (2 , - 3 , 2 )

then veca . vecb = 12 - 3 - 8 = 1

and |veca| = sqrt(6^2+1^2+(-4)^2) =sqrt(36+1+16) =sqrt53

|vecb| = sqrt(2^2+(-3)^2+2^2) = sqrt(4+9+4) = sqrt17

hence costheta = 1/(sqrt53 xx sqrt17)

theta = cos^-1 (1/(sqrt901)) = 88^@