Question Video: Multiplying Vectors by Scalars

Given that 𝐀 = βŸ¨βˆ’1, βˆ’8⟩, find 3𝐀.

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Video Transcript

Given that vector 𝐀 is equal to negative one, negative eight, find three multiplied by vector 𝐀.

In this question, we need to multiply the vector negative one, negative eight by the scalar or constant three. Let’s begin by considering the vector 𝐕 with components 𝑉 sub one and 𝑉 sub two. In order to multiply this vector by a scalar π‘˜, we multiply each of the components by that scalar. This gives us a vector with components π‘˜π‘‰ sub one and π‘˜π‘‰ sub two. We need to multiply the vector negative one, negative eight by the scalar three. Three multiplied by negative one is negative three, and three multiplied by negative eight is negative 24.

If the vector 𝐀 is equal to negative one, negative eight, then three 𝐀 is equal to negative three, negative 24. We can demonstrate this graphically. The vectors 𝐀 and three 𝐀 will travel in the same direction. However, the magnitude of three 𝐀 will be three times the magnitude of vector 𝐀.

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