### 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.