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 $\bar{a}$ ? (b) Which vectors are equal to $\bar{a}$ ?

Short Answer

Expert verified

(a) Vectors $\overset{⇀}{c}, \overset{⇀}{e}$ and $\overset{⇀}{f}$ have the same magnitude as .

(b) Vectors $\overset{⇀}{c}$ and $\overset{⇀}{f}$ are equal to .

Step by step solution

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.

Finding vectors whose magnitude is the same as a⇀

(a)

By looking at the figure, it is clear that vectors $\overset{⇀}{c}, \overset{⇀}{e}$ and $\overset{⇀}{f}$ have the same magnitude as vector $\overset{⇀}{a}$ . This is because the three rays representing these vectors have the same length as the vectorrole="math" localid="1653919248162" $\overset{⇀}{a}$ .

Therefore, the vectors $\overset{⇀}{c}, \overset{⇀}{e}$ and $\overset{⇀}{f}$ have the same magnitude as the vector $\overset{⇀}{a}$ .

Finding vectors equal to a⇀

(b)

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

Therefore, the vectors $\overset{⇀}{c}, \overset{⇀}{f}$ are equal to the vector $\overset{⇀}{a}$ .

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

Short Answer

Step by step solution

Step 1: Magnitude and direction of vectors

Finding vectors whose magnitude is the same as a⇀

Finding vectors equal to a⇀

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

Short Answer

Step by step solution

Step 1: Magnitude and direction of vectors

Finding vectors whose magnitude is the same as a⇀

Finding vectors equal to a⇀

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

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