91Ó°ÊÓ

Let A = 4i - 2j, B = -3i + 5j, and E = 2A + 3B.
a. Write vector E in component form.
b. Draw a coordinate system and on it show vectors A, B, and E .
c. What are the magnitude and direction of vector E?

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

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

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

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

Let $\stackrel{→}{E}=2\hat{i}+3\hat{j}and\stackrel{→}{F}=2\hat{i}-2\hat{j}.$Find the magnitudes of

a.$\stackrel{→}{E}and\stackrel{→}{F}$b.$\stackrel{→}{E}+\stackrel{→}{F}$c.$-\stackrel{→}{E}-2\stackrel{→}{F}$

Let $\stackrel{→}{B}=\left(5.0m,{30}^{∘}counterclockwisefromvertical\right).$Find the $xandy$-components of localid="1651138630094" $\stackrel{→}{B}$in each of the two coordinate systems shown in FIGURE EX3.18.

What are the $x$- and $y$-components of the velocity vector shown in FIGURE EX3.19?

If $\stackrel{→}{C}=\stackrel{→}{A}+\stackrel{→}{B},$Can $C>A+B?$For each, show how or explain why not

Trace the vectors in FIGURE EX3.2 onto your paper. Then find.

(a) $\stackrel{→}{A}+\stackrel{→}{B}$and (b) $\stackrel{→}{A}-\stackrel{→}{B}$localid="1649527132367" $\stackrel{→}{A}-\stackrel{→}{B}.$

For the three vectors shown in FIGURE EX3.20, $\stackrel{→}{A}+\stackrel{→}{B}+\stackrel{→}{C}=1\hat{j}.$What is vector $\stackrel{→}{B}?$

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

b. Write $\stackrel{→}{B}$as a magnitude and a direction.

The magnetic field inside an instrument is $\stackrel{→}{B}=\left(2.0\hat{i}-1.0\hat{j}\right)T,$where $\stackrel{→}{B}$represents the magnetic field vector and $T$ stands for tesla, the unit of the magnetic field. What are the magnitude and direction of the magnetic field.

Let $\stackrel{→}{A}=\left(3.0m,{20}^{∘}southofeast\right),\stackrel{→}{B}=\left(2.0mnorth\right)and\stackrel{→}{C}=\left(5.0m,{70}^{∘}southofwest\right).$ a.Draw and label $\stackrel{→}{A},\stackrel{→}{B}and\stackrel{→}{C}$with their tails at the origin. Use a coordinate system with the $x$-axis to the east.

b. Write $\stackrel{→}{A},\stackrel{→}{B}and\stackrel{→}{C}$in component form, using unit vectors.

c. Find the magnitude and the direction of$\stackrel{→}{D}=\stackrel{→}{A}+\stackrel{→}{B}+\stackrel{→}{C}.$