Question Video: Finding the Scalar Multiplied by a Vector Using a Given Figure | Nagwa Question Video: Finding the Scalar Multiplied by a Vector Using a Given Figure | Nagwa

# Question Video: Finding the Scalar Multiplied by a Vector Using a Given Figure Mathematics • First Year of Secondary School

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Given the information in the diagram below, if ππ = πππ, find π.

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### Video Transcript

Given the information in the diagram below, if ππ equals π times ππ, find π.

In our diagram, we see that the bottom side of this triangle is parallel to the line segment that runs from point πΈ to point π·. Our problem statement tells us that this vector here, from point π΅ to point π·, is equal to some constant π times the vector from π· to π΄. Itβs π we want to solve for. And to do that, letβs rearrange this equation so π is the subject.

Dividing both sides by vector ππ, this cancels on the right. And we see then that π equals ππ over ππ. Because these two vectors point in the same direction, we know that as we solve for this constant value π, itβs really the magnitudes or the lengths of these two vectors that weβre comparing. This means we can add vertical bars indicating magnitudes around the vectors of this expression. And from here we just read off these values from our diagram.

Vector ππ has a magnitude of 4.8 centimeters, and ππ has a magnitude of 7.2 centimeters. Note that in this fraction, the units will cancel out. And 4.8 divided by 7.2 simplifies to two-thirds. This is the value by which we can multiply vector ππ so that itβs equal to vector ππ.

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