Video: Evaluating Expressions Involving the Subtraction and Scalar Multiplication of Given Vectors

Given that 𝐴 = 〈0, 1βŒͺ and 𝐡 = βŒ©βˆ’3, βˆ’6βŒͺ, find (3/2)(𝐴 βˆ’ 𝐡).

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Video Transcript

Given that the vector 𝐴 is equal to zero, one and the vector 𝐡 is equal to negative three, negative six, find the vector three over two multiplied by 𝐴 minus 𝐡.

So in order to calculate this vector, we need to do two things. Firstly, we need to find the vector 𝐴 minus 𝐡. And secondly, we need to find three over two multiplied by this.

Let’s recall first of all how to find the sum or difference of two vectors. To add or subtract two vectors, we just add and subtract their component parts. So the vector π‘š, 𝑛 added or subtracted to the vector 𝑝, π‘ž will give π‘š plus or minus 𝑝, 𝑛 plus or minus π‘ž.

Therefore, to find the vector 𝐴 minus 𝐡, we need to subtract the component parts. We have zero minus negative three for the first component, one minus negative six for the second. This gives the vector three, seven for the result of 𝐴 minus 𝐡.

Next, we need to see what happens when we multiply this vector by three over two. To multiply a vector by a scalar, we just multiply each of the components by that scalar. π‘˜ multiplied by the vector π‘š, 𝑛 gives the vector π‘˜π‘š, π‘˜π‘›.

So three over two multiplied by the vector 𝐴 minus 𝐡 is equal to three over two multiplied by the vector three, seven. And we multiply three over two by each of the component parts. We have three over two multiplied by three for the first component and three over two multiplied by seven for the second. This gives our answer to the problem: the vector nine over two, 21 over two.

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