3. The components of vectors A and B are given as follows: Ax 5.1 Bx -2.6 What is the magnitude of vector sum A B A. 5.1 B. 2.5 C.-9.3 D. 9.6

You are driving up a long, inclined road. After 1.2 miles younotice that signs along the roadside indicate that your elevationhas increased by 530 ft. (a) What is the angle of the road above thehorizontal? (b) How far do you have to drive to gain an additional150 ft of elevation?

AvectorhasthecomponentsAx = 22m and Ay = 13m.(a)What is the magnitude of this vector? (b) What angle does this vector make with the positive x axis?

1. Let θ be the angle that the vector ? makes with the +x-axis, measured counterclockwise from that axis. Find angle θ for a vector that has these components: (a) Ax = 2m, Ay = -1m; (b) Ax = 2m, Ay = 1m; (c) Ax = -2m, Ay = 1m; Ax = -2m, Ay = -1m.

If the vectors A and B are perpendicular, what is the component of A along the direction of B? What is the component of B along the direction of A?

What do vectors and scalars have in common? How do they differ?

Vector F is proportional to vector A such that F=mA and m is a scalar. a. If A=2.4+3.0j and F=4.0+5.0j, what is m? b. Why is it impossible to have A=2.4+3.0j and F=4.0+0.50j, given the relationship between the two vectors?

In an attempt to escape a desert island, a castaway builds a raft and sets out to sea. The wind shifts a great deal during the day, and she is blown along the following straight lines: 2.50 km and 45.0 north of west, then 4.70 km and 60.0 south of east, then 130 km and 25.0 of west, then 5.10 km due east, then 1.70 km and 5.00 east of north, then 7.20 km and 55.0 south of west, and finally 2.80 km and 10.0 north of east. Use the analytical method to find the resultant vector of all her displacement vectors. What is its magnitude and direction?

A student claims that he has found a vector A such that (2i3j+4k)A=(4i+3j+k). (a) Do you believe this claim? (b) Explain why or why not.

Check Your Understanding Verify that vector v V obtained in Example 2.14 is indeed a unit vector by computing its magnitude. If the convoy in Example 2.8 was moving across a desert flatland—that is, it the third component of its velocity was zero—what is the unit vector of its direction of motion? Which geographic direction does it represent?