Question Video: Deciding If Two Vectors Are Parallel Mathematics

True or False: Vectors 𝐀 = 〈2, 1βŒͺ and 𝐁 = 〈6, 3βŒͺ are parallel. [A] true [B] False

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Video Transcript

True or false: vectors 𝐀 equals two, one and 𝐁 equals six, three are parallel. Option (A) true or option (B) false.

In this question, we’re given information about two vectors 𝐀 and 𝐁, and we’re asked to work out if these two vectors are parallel. We can recall that two vectors are parallel if they are scalar multiples of each other. If vectors 𝐀 and 𝐁 are parallel, then we could write that vector 𝐀 is equal to π‘˜ times vector 𝐁 for some scalar quantity π‘˜, where π‘˜ is not equal to zero. Given the information about vectors 𝐀 and 𝐁, then we can fill these into this equation and check if it’s valid. You might notice that vector 𝐁 is a nice multiple of vector 𝐀. But it’s worth checking the π‘₯- and 𝑦-components separately.

Evaluating the π‘₯-components, we’d have two is equal to six π‘˜. Dividing both sides by six would give us two-sixths is equal to π‘˜. Simplifying would give us a third equals π‘˜ or π‘˜ is equal to one-third. In order for these vectors to be parallel, then when we evaluate the 𝑦-components, we need to get the same value of π‘˜. So, let’s check. When we evaluate the 𝑦-components, we get that one is equal to three π‘˜. Dividing both sides by three, we’d get that one-third is equal to π‘˜ which, of course, means that π‘˜ is equal to one-third. We can then say that vector 𝐀 does equal π‘˜ times vector 𝐁 because we can write that vector 𝐀 is equal to one-third times vector 𝐁. We could therefore give the answer true since the statement β€œvectors 𝐀 and 𝐁 are parallel” is true.

One alternative way to answer this question would be to represent these vectors on a diagram. Vector 𝐀 is given as two, one, and vector 𝐁 is given as six, three. We can see visually that vectors 𝐀 and 𝐁 are parallel, confirming the answer that the statement is true.

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