The diagram shows two vectors X and Y, drawn to scale. If X = Y – Z, which diagram best represents the vector Z?

Question 1

The diagram shows two vectors X and Y, drawn to scale.

If X = Y – Z, which diagram best represents the vector Z?

Reference: Past Exam Paper – June 2016 Paper 12 Q3

Solution:

Answer: A.

In terms of vector diagram, we usually work with vector addition instead of subtraction. So, first, let’s try to work the equation in terms of ‘+’.

X = Y – Z = Y + (– Z)

 

From the equation, when we add the 2 vectors Y and (-Z), we obtain the resultant vector X.

To draw the vector diagram, we start by drawing a vector (vector Y). Then, we add the second vector (-Z, as in the equation) by drawing the tail of this second vector (-Z) at the head of the first vector. The resultant vector (X) starts from the tail of the vector Y to the head of vector (-Z).

Thus, the green vector represents vector (-Z). Vector Z is just in the opposite direction than vector (-Z).