Question Video: Multiplying Vectors by Scalars Mathematics

Given that 𝐀 = <−3, 2>, find −4𝐀.

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Video Transcript

Given that vector 𝐀 is equal to negative three, two, find negative four multiplied by vector 𝐀.

In this question, we need to multiply the vector negative three, two by the scalar or constant negative four. We recall that multiplying a vector by a scalar gives us another vector. If we consider vector 𝐕 with components 𝐕 sub one and 𝐕 sub two, multiplying this by the scalar 𝑘 gives us the vector with components 𝑘 𝐕 sub one, 𝑘 𝐕 sub two. We multiply the individual components by the scalar.

In this question, we need to multiply each of the components negative three and two by negative four. Negative four multiplied by negative three is equal to 12, and negative four multiplied by two is negative eight. If vector 𝐀 is equal to negative three, two, then negative four 𝐀 is equal to 12, negative eight. We can demonstrate this graphically as shown. Note that multiplying a vector by a negative scalar reverses the direction. The vector negative four 𝐀 moves in the opposite direction to the vector 𝐀 and has a magnitude four times as great.

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