Video: Multiplying Vectors by Scalars

Given that 𝐀 = ⟨6, 11⟩, find 1/2 𝐀.

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Video Transcript

Given that vector 𝐀 equals six, 11, find a half of vector 𝐀.

In this question, we need to multiply the vector with components six and 11 by the scalar or constant one-half. We recall that if vector 𝐕 has components 𝑉 sub one and 𝑉 sub two, we can calculate 𝑘 multiplied by vector 𝐕 by multiplying the scalar 𝑘 by the components 𝑉 sub one and 𝑉 sub two. This gives us a vector with components 𝑘𝑉 sub one and 𝑘𝑉 sub two.

In this question, to calculate a half of vector 𝐀, we multiply the vector six, 11 by one-half. One-half multiplied by six is equal to three, and one-half multiplied by 11 is 11 over two or 5.5. If vector 𝐀 is equal to six, 11, then a half vector 𝐀 is equal to three, 5.5. This can be demonstrated graphically. The vectors 𝐀 and a half 𝐀 travel in the same direction. However, the magnitude of vector 𝐀 is double the magnitude of a half 𝐀.

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