Some help with precalculus problems?

Question

1. Find the dot product of the two given vectors, (5,2), (0,0).
A. -3
B. 0
C. 3
D. 7

2. Find the magnitude llvll of v(2,3).
A. 1
B. sqrt(5)
C. Sqrt(13)
D. 5

3. Find the sum of the two given vectors, (5,-2) and (0,0).
A. (0,0)
B. (-5,2)
C. (10,-4)
D. (5,-2)

4. Find the dot product v=2i + 6j and w=-5i-2j.
A. -22
B. -2
C. 2
D. 22

Please give explanation of how you got the answer. Thanks.

Answer 1

1) Dot product:

v = (5,2), u = (0,0)

v ∙ u = <v1, v2> ∙ <u1, u2> = v1u1 + v2u2

v∙u = 5*0 + 2* 0 = 0

The answer is B.

2) v = <2, 3>

||v|| =  √ [(v1)² + (v2)² ]

= √ [(2)² + (3)² ]

= √ [4 + 9]

= √13

The answer is C.

3) v = (5,-2), u = (0,0)

v + u = <v1, v2> + <u1, u2> = <v1+u1, v2+u2>

= (5 + 0, -2 + 0)

= (5, -2)

The answer is D.

4) v = 2i + 6j = (2, 6),

u =-5i - 2j = (-5, -2).

v ∙ u = <v1, v2> ∙ <u1, u2> = v1u1 + v2u2

= 2*-5 + 6*-2

= -10 - 12

= -22.

The answer is A.