Question

A vector R is given by\[R = A \times \left( {B \times C} \right)\], which of the following is true?
A. R must be perpendicular to B.
B. R is parallel to A.
C. R must be parallel to B.
D. None of the above.

Answer 1

Hint: There are two types of quantities which are scalar quantity and the vector quantity. The quantity which shows only magnitude is called the scalar quantity and the quantity which shows magnitude as well as direction is called the vector quantity. It is to be noted that the vectors are also used to define the imaginary quantities using a symbol “i”. Sometimes there will be large values that are unable to calculate so such values are defined using the vectors.

Complete step-by-step answer:
A vector perpendicular to a given vector is a vector (voiced " -perp") such that and. form a right angle. In the plane, there are two vectors perpendicular to any given vector, one rotated counterclockwise and the other rotated clockwise.
The vector R is given by \[R = A \times \left( {B \times C} \right)\].
It is clear that whenever the two vectors are perpendicular to the third then they are denoted as,\[R = A \times \left( {B \times C} \right)\]
Where, R is perpendicular to the A and R is perpendicular to the B and C simultaneously.
Therefore, the answer is R is perpendicular to both A and \[B \times C\] .
So, the correct answer is “Option D”.

Note: Here, the given vectors contain a certain relation between them so they are denoted in \[R = A \times \left( {B \times C} \right)\] form. We have to be aware about the relations like parallel and perpendicular to form any equation between vectors using them. As these vectors are related as perpendicular to each other, so they form an equation using multiplication symbols.