# Question Video: Finding the Direction Vector of the Line of Intersection of Two Planes Mathematics

Two motorcycles A and B, are moving in the same direction. If the velocity of A is 30 km/h and the velocity of B is 15 km/h, find the relative velocity of A with respect to B.

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### Video Transcript

Two motorcycles A and B are moving in the same direction. If the velocity of A is 30 kilometers per hour and the velocity of B is 15 kilometers per hour, find the relative velocity of A with respect to B.

In this example, we want to find the relative velocity of motorcycle A and that of motorcycle B which are traveling in the same direction. To calculate this, we recall 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 that π A minus π B.

If we let the velocity of motorcycle A be π A, which is 30 kilometers per hour, and the velocity of motorcycle B be π B, and thatβs 15 kilometers per hour β noting that since the motorcycles move in the same direction, theyβll have the same sign β then the relative velocity of motorcycle A with respect to B is π A minus π B, which is 30 minus 15. And thatβs 15. Hence, the relative velocity of motorcycle A with B is 15 kilometers per hour.