91Ó°ÊÓ

Can the magnitude of the displacement vector be more than the distance traveled? Less than the distance traveled? Explain

Trace the vectors in FIGURE EX3.1 onto your paper. Then find.

(a)$\stackrel{→}{A}+\stackrel{→}{B}$and (b)$\stackrel{→}{A}-\stackrel{→}{B}.$

1. I Trace the vectors in FIGURE EX3.1 onto your paper. Then find

(a) $\stackrel{→}{A}+\stackrel{→}{B}$and (b) $\stackrel{→}{A}−\stackrel{→}{B}$

II Draw each of the following vectors, label an angle that specifies the vector's direction, then find its magnitude and direction.

a.$B=−4\widehat{i}+4\widehat{j}$

b.$\stackrel{→}{r}=(−2.0\widehat{i}−1.0\widehat{j})\text{cm}$

c.$\stackrel{→}{v}=(−10\widehat{i}−100\widehat{j})\text{m}/\text{s}$

d.$a=(20\widehat{i}+10\widehat{j})\text{m}/{\text{s}}^2$

II Draw each of the following vectors, label an angle that specifies the vector's direction, and then find the vector's magnitude and direction.

a.$\stackrel{→}{A}=3\widehat{i}+7\widehat{j}$

b.$a=(−2\widehat{i}+4.5\widehat{j})\text{m}/{\text{s}}^2$

c.$\stackrel{→}{v}=(14\widehat{i}−11\widehat{j})\text{m}/\text{s}$

d.$\stackrel{→}{r}=(−2.2\widehat{i}−3.3\widehat{j})\text{m}$

Let, $\stackrel{→}{A}=2\hat{i}+3\hat{j},\stackrel{→}{B}=2\hat{i}-4\hat{j}and\stackrel{→}{C}=\stackrel{→}{A}+\stackrel{→}{B}.$

a. Write vector $\stackrel{→}{C}$in component form.

b. Draw a coordinate system and on it show vectors $\stackrel{→}{A},\stackrel{→}{B}and\stackrel{→}{C}.$

c. What are the magnitude and direction of vector$\stackrel{→}{C}?$

Let, $\stackrel{→}{A}=4\hat{i}-2\hat{j},\stackrel{→}{B}=-3\hat{i}+5\hat{j}and\stackrel{→}{C}=\stackrel{→}{A}+\stackrel{→}{B}.$

a. Write vector $\stackrel{→}{C}$in component form.

b. Draw a coordinate system and on it show vectors $\stackrel{→}{A},\stackrel{→}{B}and\stackrel{→}{C}.$

c. What are the magnitude and direction of the vector$\stackrel{→}{C}?$

Let $\stackrel{→}{A}=4\widehat{i}−2\widehat{j}$, $\stackrel{→}{B}=−3\widehat{i}+5\widehat{j}$and $C=A+B$.

a. Write vector $\stackrel{→}{C}$in component form.

b. Draw a coordinate system and on it show vectors$\stackrel{→}{A},\stackrel{→}{B}$, and$\stackrel{→}{C}$.

c. What are the magnitude and direction of vector $\stackrel{→}{C}$?

Let $\stackrel{→}{A}=4\hat{i}-2\hat{j},\stackrel{→}{B}=-3\hat{i}+5\hat{j}and\stackrel{→}{D}=\stackrel{→}{A}-\stackrel{→}{B}.$

a. Write vector $\stackrel{→}{D}$in component form.

b. Draw a coordinate system and on it show vectors $\stackrel{→}{A},\stackrel{→}{B},and\stackrel{→}{D}.$

c. What are the magnitude and direction of vector$\stackrel{→}{D}?$

Let $\stackrel{→}{A}=4\widehat{i}−2\widehat{j}$,$\stackrel{→}{B}=−3\widehat{i}+5\widehat{j}$ and $\stackrel{→}{D}=\stackrel{→}{A}−\stackrel{→}{B}$.

a. Write vector $\stackrel{→}{D}$in component form.

b. Draw a coordinate system and on it show vectors$\stackrel{→}{A},\stackrel{→}{B}$, and$\stackrel{→}{D}$.

c. What are the magnitude and direction of vector $\stackrel{→}{D}$?