# Question Video: Finding the Relative Velocity between Two Bodies Moving in Opposite Directions in Vector Form Mathematics

Two cars A and B are moving in opposite directions on the same road at 62 km/h and 31 km/h respectively. Given that π is a unit vector in the direction of movement of car A, determine the velocity of car A relative to car B.

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### Video Transcript

Two cars A and B are moving in opposite directions on the same road at 62 kilometers per hour and 31 kilometers per hour, respectively. Given that π is a unit vector in the direction of movement of car A, determine the velocity of car A relative to car B.

Weβre asked to determine the relative velocity of car A with respect to car B and given that π is a unit vector in the direction of car A. Weβre told the car A is moving at 62 kilometers per hour and car B is moving at 31 kilometers per hour in the opposite direction. The velocity of car A is then 62π. And since car B is moving in the opposite direction, its velocity π B is negative 31π.

Now recalling that for two bodies A and B moving with velocities π A and π B, respectively, the relative velocity of A with respect to B is π AB and thatβs π A minus π B. In our case, thatβs 62π, which is π A, minus negative 31π, which is π B. 62 minus negative 31 is 62 plus 31. And so we have 93π. The velocity of car A relative to car B is 93π kilometers per hour.