PHYENG 1ST EXAM

What is the minimum number of vectors with unequal magnitudes whose vector sum can be zero?

• two

• three

• four

• six

Two vectors A and B are added together to form a vector C. The relationship between the magnitudes of the vectors is given by:  $A^2$  +  $B^2$  =  $C^2$ . Which statement concerning these vectors is true?

• A and B must be at right angles to each other.

• They could have any orientation relative to each other.

• A and B must have equal lengths.

• A and B must be parallel.

Given the vector A = 100.00 N at 30.00⁰ above the negative x- axis. In terms of rectangular form, the vector can also be expressed as

• A = -86.60 i + 50.00 j

• A = 86.60 i - 50.00 j

• A = -50.00 i + 86.60 b j

• A = 50.00 i _ 86.60 j

Three vectors A, B, and C have the following x and y components: A_x = 1 m, A_y = 0; B_x = 1 m, B_y = 1 m; C_x = 0,

C_y = - 1m. According to the graph, how are A, B, and C are combined to give a resultant vector D?

• D = A - B - C

• D = A - B + C

• D = A + B - C

• D = A + B + C

Vectors i, j, and k are unit vectors directed positively along the x-,y- and z-axes, respectively. The dot product j  $\cdot$  j is equal to

• 0

• 1

• i

• k

Two force vectors of magnitudes 21 N and 79 N are added. Which one of the following is the only possible choice of the magnitude of the resultant?

• 0 N

• 28 N

• 114 N

• 82 N

The magnitude of a unit vector  $\lambda$  is

• 0

• 1

• -1

• 2

Which of the following is not correct?

• j x j = 0

• j x k = i

• j x i = k

• j x i = -k

Given: A = 2i - 3j + k, B = i - j + k, C = i - 3j + 2k,
and D = 4i + 2k
The scalar product D  $\cdot$  A

• 7

• 11

• 8

• 10

Given: A = 2i - 3j + k, B = i - j + k,

C = i - 3j + 2k, and D = 4i + 2k

What is the angle between A and D ?

• 47.63⁰

• 53.30⁰

• 67.82⁰

• 112.34⁰