Question

Which of the following expressions does not make sense?
u, v, w are vectors.
A. $ (u + v) \times (u - w) $
B. $ \left| {\left. u \right| \times (w - v)} \right. $
C. $ \left| {\left. u \right|(v \times w)} \right. $
D. $ u + (v - w) $

Answer 1

Hint: Here we solve this question by checking each and every option. The option which does not exist is the answer for this question. To solve this question we should primarily know about cross products which we have studied in high school.

Complete step-by-step answer:
A vector is an object that has both a magnitude and a direction. Geometrically, we can picture a vector as a directed line segment, whose length is the magnitude of the vector and with an arrow indicating the direction

A. $ (u + v) \times (u - w) $ is a cross product of 2 vectors hence, this option does make sense.
B. $ \left| {\left. u \right| \times (w - v)} \right. $ , Here \[|u|\]is a scalar and $ (w - v) $ is a vector. Cross product is product of two vectors. Hence, this option does not make sense.
C. $ \left| {\left. u \right|(v \times w)} \right. $ , is a scalar multiplication of a vector. Hence it makes sense.
D. $ u + (v - w) $ is subtraction and addition of vectors ,Hence it is possible.
So, the correct answer is “Option B”.

Note: Cross product also known as vector product as it results in a vector as an answer. Cross product of vectors a and b is given by
 $ a \times b = |a||b|\sin \theta $ , where $ \theta $ is the angle between vectors a and b.