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Chapter 1: Q12CP (page 39)

Figure 1.55 shows several arrows representing vectors in the xy plane. (a) Which vectors have magnitudes equal to the magnitude of a炉? (b) Which vectors are equal to a炉?

Short Answer

Expert verified

(a) Vectors c鈬赌,e鈬赌and f鈬赌 have the same magnitude as .

(b) Vectors c鈬赌and f鈬赌are equal to .

Step by step solution

01

Step 1: Magnitude and direction of vectors

While comparing the magnitude of vectors, one can compare the length of the rays.

To check the equality of vectors, both the direction and length of rays must be the same.

02

Finding vectors whose magnitude is the same as a⇀

(a)

By looking at the figure, it is clear that vectorsc鈬赌,e鈬赌 andf鈬赌have the same magnitude as vectora鈬赌. This is because the three rays representing these vectors have the same length as the vectorrole="math" localid="1653919248162" a鈬赌.

Therefore, the vectorsc鈬赌,e鈬赌andf鈬赌have the same magnitude as the vectora鈬赌.

03

Finding vectors equal to  a⇀

(b)

It is evident from the figure that vectorsc鈬赌andf鈬赌have the same direction and magnitude as vectora鈬赌. So, both these are equal to vectora鈬赌.

Therefore, the vectors c鈬赌,f鈬赌 are equal to the vector a鈬赌.

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Figure 1.20

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