Question

Find the angle between the vectors. (first find an exact expression and then approximate to the nearest degree.) a = 5, −1, 7 , b = −2, 4, 3

Answer 1

a.b=lallbl cos t
a.b=(-2*5)+(-1*4)+(3*7)
a.b=7

lal=√(25+1+49)=5√3
lbl=√(4+16+9)=√29
therefore:
7=5√3×√29 cost
cost=0.1501
t=arccos 0.1501=81.37°