Using the formula

angle between vectors

we find the dot product first:

P • Q

= (3 i + 4 j − 7 j) • (-2 i + j + 3 k )

= (3 × -2) + (4 × 1) + (-7 × 3)

= -23

And now for the denominator:

|P| |Q|  

= √(32 + 42 + (-7) 2) × √((-2)2 + 1 2 + 32)

= 32.187

So

θ = arccos(-23 ÷ 32.187)

Therefore the angle between the vectors P and Q is

θ = 135.6°