If P→=3i^+5j^+2k^  , Q→=5i^−j^+4k^  and R→=4i^+2j^+3k^ are coplanar, then:

The scalar triple product P→.(Q→×R→)=(P→×Q→).R→  for three coplanar vectors is always zero, as it represents the volume of parallelepiped formed with three adjacent sides as the vectors P→,Q→  and R→ . Here P→×Q→=(3i^+5j^+2k^)×(5i^−j^+4k^) =| i^     j^     k^  3     5     2  5   −1    4 | =i^(20+2)−j^(12−10)+k^(−3−25) =22i^−2j^−28k^ (P→×Q→).R→=(22i^−2j^−28k^).(4i+2j^+3k^) =88−4−84=zero .