# 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 𝑉 A and 𝑉 B, respectively, the relative velocity of A with respect to B is 𝑉 AB and that 𝑉 A minus 𝑉 B.

If we let the velocity of motorcycle A be 𝑉 A, which is 30 kilometers per hour, and the velocity of motorcycle B be 𝑉 B, and that’s 15 kilometers per hour — noting that since the motorcycles move in the same direction, they’ll have the same sign — then the relative velocity of motorcycle A with respect to B is 𝑉 A minus 𝑉 B, which is 30 minus 15. And that’s 15. Hence, the relative velocity of motorcycle A with B is 15 kilometers per hour.

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