3. Vectors

Which of the following correctly expresses the vector $b$ using unit vectors in Cartesian coordinates?

A = (4.0 m)i + (3.0 m)j and B = (−13.0 m)i + (7.0 m)j. You add them together to produce another vector C.
(a) Express this new vector C in unit-vector notation.
(b) What are the magnitude and direction of C?

In each case, find the x- and y- components of vector A: A = 11.2j - 9.91i

Given two vectors A = -2i + 3j + 4k and B = 3.00î + 1.00ĵ − 3.00k, find the magnitude of each vector.

You are given two vectors A = -3i + 6j and B = 7i + 2j. Let Counterclockwise angles be positive. What angle does A make with the +x-axis?

Given two vectors A = 4i + 7j and B = 5i - 2j, find the magnitude of each vector.

Trevon drives with velocity v₁ = (55î - 10ĵ) mph for 1.0 h, then v₂ = (20î ＋ 50ĵ) mph for 2.0 h. What is Trevon's displacement? Write your answer in component form using unit vectors.

Let E = 2i + 3j and F = 2i - 2j. Find the magnitude of -E - 2F.

What are the x- and y-components of vector E shown in FIGURE EX3.3 in terms of the angle θ and the magnitude E?

A cannonball leaves the barrel with velocity v = (75î ＋ 45ĵ). At what angle is the barrel tilted above horizontal?

The position of a particle as a function of time is given by $\overrightarrow{r}$ = ( 5.0î ＋4.0ĵ )t² m where t is in seconds. What is the particle's speed at t = 0, 2, and 5 s?

The position of a particle as a function of time is given by $\overrightarrow{r}$ = ( 5.0î ＋4.0ĵ )t² m where t is in seconds. Find an expression for the particle's velocity $\overrightarrow{v}$ as a function of time.

The position of a particle as a function of time is given by $\overrightarrow{r}$ = ( 5.0î ＋4.0ĵ )t² m where t is in seconds. What is the particle's distance from the origin at t = 0, 2, and 5 s?

Let E = 2i + 3j and F = 2i - 2j. Find the magnitude of E and F.

Find a vector that points in the same direction as the vector ( î ＋ ĵ ) and whose magnitude is 1.