2 4 3 3 4 1 4 -3 5 1 −1 1 −2 3 2

Vector A = (8, 4, -5) and Vector B = (-2, 3, 0). Find the angle between these two vectors.

Vector G is 40.3 m long in a -35.0° direction. Vector H is 63.3 m long in a 270° direction. Find the magnitude of their vector sum. magnitude (m) Enter

A vector v has initial point P₁ = (-1,2) and terminal point P₂ = (x, 14). Find all numbers x so that v has length 13. (Express numbers in exact form. Use symbolic notation and fractions where needed. Give your answer in the form of a comma separated list if needed.) X=

2 Use the determinant of a matrix to find the area of the triangle whose vertices are (6, 1), (8,5), and (3, 1). ▸ Area = W S Enter an integer or decimal number [more..] Calculator Check Answer X 36 3 20 F3 E $ 4 D 이 C F4 R F % 5 F5 V T MacBook Air A 6 G F6 Y B & 7 H AK F7 C * 00 8 N DII FB - ( 9 F9 K M O V F10 X

Say that a is a vector (nonzero) in the third dimension. b and c are two other vectors. If a • b = a • c, and a x b = a x c, is b = c?

A vector has a magnitude of 2.8 m and points in a direction that is 135 counterclockwise from the a axis. You may want to review (Page 71).

Determine the direction of vector V measured counterclockwise from the positive x-axis. Given: V(x) =9.6  &   V(y)= -6.1

Consider two vectors A and B such that Ã × B – B (÷ B Find the angle between A and B if ß = 6. O Report your numerical answer below, assuming three significant figures.

1. ANALYTICAL METHOD OF ADDING VECTORS Solve the same problem as PART 1 but this time analytically. START with the values below. DO NOT USE VALUES FROM PART 1. Suppose you first walk A = 12 m in a direction 20° west of north and then B= 20 m in a direction 40° south of west. Let the +x-axis coincide with the easterly direction and the +y-axis with the northerly direction. Note: In this problem, do not round values if you need to use them for calculations in subsequent parts. Rounding errors can propagate and can make your final answer lie outside the tolerance limit of 5% set for this problem. Keep all answers to 4 significant figures.