Using the formula

`theta=arccos((P*Q)/(|P||Q|))`

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 + 12 + 32)

= 32.187

So

θ = arccos(−23 ÷ 32.187)

Therefore the angle between the vectors P and Q is

θ = 135.6°

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