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

1 Answer
Jim G.
Jan 28, 2016

88^@ 88∘

Explanation:

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

costheta =( veca.vecb)/((|veca| xx |vecb|) cosθ=→a.→b(∣∣→a∣∣×∣∣∣→b∣∣∣)

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

let veca = (6,1,-4) , vecb = (2 , - 3 , 2 ) →a=(6,1,−4),→b=(2,−3,2)

then veca . vecb = 12 - 3 - 8 = 1 →a.→b=12−3−8=1

and |veca| = sqrt(6^2+1^2+(-4)^2) =sqrt(36+1+16) =sqrt53∣∣→a∣∣=√62+12+(−4)2=√36+1+16=√53

|vecb| = sqrt(2^2+(-3)^2+2^2) = sqrt(4+9+4) = sqrt17 ∣∣∣→b∣∣∣=√22+(−3)2+22=√4+9+4=√17

hence costheta = 1/(sqrt53 xx sqrt17) cosθ=1√53×√17

theta = cos^-1 (1/(sqrt901)) = 88^@θ=cos−1(1√901)=88∘

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