Question Video: Scalar Multiplication of a Vector Mathematics

Given that π = β¨6, 11β©, find 1/2 π.

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Video Transcript

Given that π is the vector six, 11, find a half π.

In this question, we have a vector π. And this vector is given component-wise. Weβre asked to find the value of one-half times π. So weβre asked to find the product between a constant and a vector. We can do this by using scalar multiplication. To do this, we need to recall for constant π and vector π, π, π times the vector π, π is equal to the vector ππ, ππ. In other words, we multiply each of the components of our vector by our value of π.

So to evaluate one-half multiplied by π, we want to multiply each of the components of π by one-half. This gives us the vector one-half times six, one-half times 11. And we can evaluate each of these components separately. One-half times six is equal to three, and one-half times 11 is equal to 5.5. This gives us our final answer of the vector three, 5.5.

Therefore, we were able to show if π is the vector six, 11, then we can evaluate one-half multiplied by π by multiplying each component by one-half. We got one-half π is equal to the vector three, 5.5.