Question Video: Solving Problems Involving Parallel and Perpendicular Vectors in 2D

If 𝚨 = −4𝚩, then _.

01:46

Video Transcript

If vector 𝚨 is equal to negative four multiplied by vector 𝚩, then which of the statements is true? Is it (A) four multiplied by vector 𝚨 is equal to vector 𝚩? Option (B) the magnitude of vector 𝚨 is equal to the magnitude of vector 𝚩. Is it option (C) the vectors 𝚨 and 𝚩 are parallel? Or option (D) the vectors 𝚨 and 𝚩 are perpendicular.

If vector 𝚨 is equal to negative four multiplied by vector 𝚩, then dividing both sides of our equation by negative four, we see that vector 𝚩 is equal to negative one-quarter multiplied by vector 𝚨. This immediately rules out option (A) as the correct answer as this stated that vector 𝚩 was equal to four multiplied by vector 𝚨.

In order to decide which of the other three options is correct, we need to recall one of our key definitions when dealing with vectors. We know that if two vectors 𝚨 and 𝚩 are parallel, then vector 𝚨 is equal to some nonzero constant 𝑘 multiplied by vector 𝚩. In this question, we are told that vector 𝚨 is equal to the constant or scalar negative four multiplied by vector 𝚩. This means that vector 𝚨 and vector 𝚩 are parallel. The correct answer is option (C). If 𝚨 is equal to negative four multiplied by 𝚩, then vector 𝚨 and vector 𝚩 are parallel.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.