Question

please answer all of them a. Suppose u and v are non-zero, parallel vectors. Which of...

please answer all of them

a. Suppose u and v are non-zero, parallel vectors. Which of the following could not possibly be true?

a)

 u • v = |u | |v|

b)

 u + v = 0

c)

 u × v = |u|2

d)

 |u| + |v| = 2|u|

b. Given points A(3, -4, 2) and B(-12, 16, 12), point P, lying between A and B such that AP= 3/5AB would have coordinates

a)

 P(-27/5, 36/5, 42/5)

b)

 P(-6, 8, 8)

c)

 P(-9, 12, 6)

d)

 P(-36/5, 48/5, 36/5)

c. A vector of length 5 perpendicular to both u = (3, -1, 5) and v =(2, 1, 0) has coordinates

i. (-25/sqrt150, 50/sqrt150, 25/sqrt150)

ii. (-25,50,25)

iii. (-5/sqrt150, 10/sqrt150, 5/sqrt150)

iv. (-5,10,5)

d. If u, v and w are mutually perpendicular vectors, which of the following would not be true?

a)

 v • (u - w) = 0

b)

 w • (v + u) = 0

c)

 v • (w × u) = 0

d)

 (u × v) • (u × w) = 0

e. The derivative of (x4 - 2)5 is

a)

 5(4x3)4

b)

 5(4x4 - 2)4

c)

 20x3(x4 - 2)4

d)

 20x(x4 - 2)4

f. Which of the following is not an equivalent way of expressing the term "derivative?"

a)

 average rate of change

b)

 slope of the tangent

c)

 slope of the curve

d)

 instantaneous rate of change
Math   Calculus   
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