operating with displacements according to the rules for manipulating vectors leads to results in agreement with experiments
We say that the displacement of a particle is a vector quantity. Our best justification for this assertion is
D
Ch 3 #2
The vectors a, b, and c are related by c = b – a. Which diagram below represents this relationship?
zero
A vector of magnitude 3 CANNOT be added to a vector of magnitude 4 so that the magnitude of the resultant is
12
A vector of magnitude 20 is added to a vector of magnitude 25. The magnitude of this sum might be
must have a magnitude of at least 6 but no more than 18
A vector S of magnitude 6 and another vector T have a sum of magnitude 12. The vector T
in the direction opposite to A
The vector -A is
V2 – V1
Ch 3 #7
The vector V3 in the diagram is equal to
none of the above is true
If |A+B|^2 = A^2 + B^2, then
A and B are parallel and in the same direction
If |A+B| = A + B and neither A nor B vanish, then
A and B are parallel and in opposite directions
If |A-B| = A+B and neither A nor B vanish, then
B + D – √2C = 0
Ch 3 #11
Four vectors (A, B, C, D) all have the same magnitude. The angle θ between adjacent vectors is 45˚ as shown. The correct vector equation is
Ax=Bx and Ay=By
Vectors A and B lie in the xy plane. We can deduce that A = B if
-6
A vector has a magnitude of 12. When its tail is at the origin it lies between the positive x axis and the negative y axis and makes an angle of 30˚ with the x axis. Its y component is
3/2
If the x component of a vector A, in the xy plane, is half as large as the magnitude of the vector, the tangent of the angel between the vector and the x axis is
40 m
If A = (6m)i – (8m)j then 4A has magnitude
15m
A vector has a component of 10m in the +x direction, a component of 10m in the +y direction, and a component of 5m in the +z direction. The magnitude of this vector is
7.00m
Let V = (2.00m)i + (6.00m)j – (3.00m)k. The magnitude of V is
61˚
A vector in the xy plane has a magnitude of 25m and an x component of 12m. The angle it makes with the positive x axis is
61˚
The angle between A = (25m)i + (45m)j and the positive x axis is
119˚
The angle between A = (-25m)i + (45m)j and the positive x axis is
(6m)i + (8m)j – (2m)k
Let A = (2m)i + (6m)j – (3m)k and B = (4m)i + (2m)j + (1m)k. The vector sum S = A + B is
(-2m)i + (4m)j – (4m)k
Let A = (2m)i + (6m)j – (3m)k and B = (4m)i + (2m)j + (1m)k. The vector difference D = A – B is
(1m)j
If A = (2m)i – (2m)j and B = (1m)i – (2m)j, then A – 2B =
12 m
Ch 3 #24
In the diagram, A has a magnitude 12m and B has magnitude 8m. The x component of A + b is about
7.2m
A certain vector in the xy plane has an x component of 4m and a y component of 10m. It is then rotated in the xy plane so its x component is doubled. Its new y component is about
√3L^2/2
Vectors A and B each have magnitude L. When drawn with their tails at the same point, the angle between them is 30˚. The value of A•B is
17 m^2
Let A = (2m)i + (6m)j – (3m)k and B = (4m)i + (2m)j + (1m)k. Then A•B =
6.3m
Two vectors have magnitudes 10m and 15m. The angle between them when they are drawn with their tails at the same point is 65˚. The component of the longer vector along the line of the shorter is
cos^-1(11/15)
Let S = (1m)i + (2m)j + (2m)k and T = (3m)i + (4m)k. The angle between these two vectors is given by
80˚
Two vectors lie with their tails at the same point. When the angle between them is increased by 20˚ their scalar product has the same magnitude but changes from positive to negative. The original angle between them was
the scalar product of the vectors must be negative
If the magnitude of the sum of two vectors is less than the magnitude of either vector, then
none of the above
If the magnitude of the sum of two vectors is greater than the magnitude of either vector, then
√3L^2/2
Vectors A and B each have magnitude L. When drawn with their tails at the same point, the angle between them is 60˚. The magnitude of the vector product AxB is
18˚
Two vectors lie with their tails at the same point. When the angle between them is increased by 20˚ the magnitude of their vector vector product doubles. The original angle between them was about
14m
Two vectors have magnitudes of 10m and 15m. The angle between them when they are drawn with their tails at the same point is 65˚. The component of the longer vector along the line perpendicular to the shorter vector, in the plane of the vectors, is
(4m)i + (6m)j + (13m)k
The two vectors (3m)i – (2m)j and (2m)i + (3m)j-(2m)k define a plane. It is the plane of the triangle with both tails at one vertex and each head at one of the other vertices. Which of the following vectors is perpendicular to the plane?
S•T=0
Let R = SxT and θ ≠ 90˚, where θ is the angle between S and T when they are drawn with their tails at the same point. Which of the following is NOT true?
+1
The value of i•(j x k) is
zero
The value of k • (k x i) is
