Question

Figure 1.55 shows several arrows representing vectors in the xy plane. (a) Which vectors have magnitudes equal to the magnitude of $\stackrel{\rightharpoonup }{a}$? (b) Which vectors are equal to $\stackrel{\rightharpoonup }{a}$?

Short answer

(a) Vectors and have same magnitude as .

(b) Vectors and are equal to .

Step-by-step solution

Magnitude and direction of vectors 

While comparing magnitude of vectors, one can compare the length of the rays.To check equality of vectors, both direction and length of rays must be same.

Finding vectors whose magnitude is same as 

(a)

By looking at the figure, it is clear that vectors $\stackrel{\rightharpoonup }{c},\stackrel{\rightharpoonup }{e}$and $\stackrel{\rightharpoonup }{f}$have same magnitude as of vector $\stackrel{\rightharpoonup }{a}$. This is because the three rays representing these vectors have same length as that of vector$\stackrel{\rightharpoonup }{a}$ .

Therefore, the vectors $\stackrel{\rightharpoonup }{c},\stackrel{\rightharpoonup }{e}$and $\stackrel{\rightharpoonup }{f}$have same magnitude as $\stackrel{\rightharpoonup }{a}$.

Finding vectors equal to a⇀ 

(b)

It is clearly evident from the figure that vectors $\stackrel{\rightharpoonup }{c}$and $\stackrel{\rightharpoonup }{f}$have same direction and magnitude as of vector $\stackrel{\rightharpoonup }{a}$. So, both these are equal to vector $\stackrel{\rightharpoonup }{a}$.

Therefore, the vectors $\stackrel{\rightharpoonup }{c}$and $\stackrel{\rightharpoonup }{f}$are equal to $\stackrel{\rightharpoonup }{a}$.