I need the answer for 42,43,44,45,46,47,48,49 step by step if possible 42. Suppose a and b are vectors such that a x b = (3, 1, 4). What is the cross product of twice of a with twice ofb ?(3, 1, 4)b. (6, 2, 8)(12, 4, 16)d. (0, 0, 0)a.с.43. If ABC is a triangle with vertices A(2, 1, 4), B(2, 0, 1), and C(3, 0, 2), then what is AB × BC ?(2, 8, -3)b. (-2, -8, 3)(1, 3, -1)d. (-1, -3, 1)a.с.44. What is the area of the parallelogram formed by the vectors a = (1, 0, 2) and b = (0, -1, 2)?a. 3c.2b. 9d.45. A bolt is being loosened by a 40 cm wrench. The torque in this situation has a magnitude of 12 J and the forcemakes an angle of 60° with the wrench. What is the magnitude of the force used to loosen the bolt?2.4 Na.с.34.6 Nb.4.2 Nd.60.0 N46. Determine the equation of the line through the origin and the point P( 10,3).7 = s(10,3), sr =s(-3,10), s e R$(3,10), s47. Determine the vector and parametric equations for the line passing through the points P(-1,-3) and Q(3,5).а.c.b. x = 3t, y = 10t, t e Rd.,SE R=7= (3,5) +s(1,2), sx = 21 – 1, y = 41 – 3, t e R7= (1,0) +s(2,4), sx = 1-1, y = 21 – 3, t e RSE RSERа.с.3 (1,-3) +s(4,8), -x = 41 – 1, y = 8t – 3, t e Rb.r =SERd. all of the above48. Determine the point of intersection of the lines L,: r = (1,3,7) + s(1,2,-2), s e R and L,:= (0,2,-3) +1(1,1,4), 1 e R.P(1,3,1)b. P(1,3,7)yC.The lines coincide.a.d.no point of intersectionx+2 y-3 z-249. Determine the parametric equation of the plane that contains the line5and the point2%3D%3D3P(2,5,3).a. x = 2+ 5s + 4t, y = 5 + 3s + 2t, z = 3 + 2s + t, s,t e Rb. x = 2+ 5s + 3t, y = 5 +3s + 2t, z = 4 + 2s + t, s,t e Rc. x = -2+5s +2t, y = 3+3s + 5t, z = 2+ 2s + 3t, s,t e Rd. x = 5+2s + 2t, y = 3– 3s + 5t, z = 2 – 2s + 3t, s,t e R

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Description: I need the answer for 42,43,44,45,46,47,48,49 step by step if possible 42. Suppose a and b are vectors such that a x b = (3, 1, 4). What is the cross product of twice of a with twice ofb ?(3, 1, 4)b. (6, 2, 8)(12, 4, 16)d. (0, 0, 0)a.с.43. If ABC is

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42. Suppose a and b are vectors such that a x b (3, 1, 4). What is the cross product of twice of a v b? a. (3, 1, 4) b. (6, 2, 8) c. (12, 4, 16) d. (0, 0, 0) 43. If ABC is a triangle with vertices A(2, 1, 4), B(2, 0, 1), and C(3, 0, 2), then what is AB × BC ? a. (2, 8, -3) b. (-2, -8, 3) c. (1, 3, –1) d. (-1,-3, 1) 44. What is the area of the parallelogram formed by the vectors a = (1, 0, 2) and b = (0, -1, 2)? 3 3 с. a.

42. Suppose a and b are vectors such that a x b (3, 1, 4). What is the cross product of twice of a v b? a. (3, 1, 4) b. (6, 2, 8) c. (12, 4, 16) d. (0, 0, 0) 43. If ABC is a triangle with vertices A(2, 1, 4), B(2, 0, 1), and C(3, 0, 2), then what is AB × BC ? a. (2, 8, -3) b. (-2, -8, 3) c. (1, 3, –1) d. (-1,-3, 1) 44. What is the area of the parallelogram formed by the vectors a = (1, 0, 2) and b = (0, -1, 2)? 3 3 с. a.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.

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Question

I need the answer for 42,43,44,45,46,47,48,49 step by step if possible

42. Suppose a and b are vectors such that a x b = (3, 1, 4). What is the cross product of twice of a with twice of
b ?
(3, 1, 4)
b. (6, 2, 8)
(12, 4, 16)
d. (0, 0, 0)
a.
с.
43. If ABC is a triangle with vertices A(2, 1, 4), B(2, 0, 1), and C(3, 0, 2), then what is AB × BC ?
(2, 8, -3)
b. (-2, -8, 3)
(1, 3, -1)
d. (-1, -3, 1)
a.
с.
44. What is the area of the parallelogram formed by the vectors a = (1, 0, 2) and b = (0, -1, 2)?
a. 3
c.
2
b. 9
d.
45. A bolt is being loosened by a 40 cm wrench. The torque in this situation has a magnitude of 12 J and the force
makes an angle of 60° with the wrench. What is the magnitude of the force used to loosen the bolt?
2.4 N
a.
с.
34.6 N
b.
4.2 N
d.
60.0 N
46. Determine the equation of the line through the origin and the point P( 10,3).
7 = s(10,3), s
r =s(-3,10), s e R
$(3,10), s
47. Determine the vector and parametric equations for the line passing through the points P(-1,-3) and Q(3,5).
а.
c.
b. x = 3t, y = 10t, t e R
d.
,SE R
=
7= (3,5) +s(1,2), s
x = 21 – 1, y = 41 – 3, t e R
7= (1,0) +s(2,4), s
x = 1-1, y = 21 – 3, t e R
SE R
SER
а.
с.
3 (1,-3) +s(4,8), -
x = 41 – 1, y = 8t – 3, t e R
b.
r =
SER
d. all of the above
48. Determine the point of intersection of the lines L,: r = (1,3,7) + s(1,2,-2), s e R and L,:
= (0,2,-3) +1(1,1,4), 1 e R.
P(1,3,1)
b. P(1,3,7)
y
C.
The lines coincide.
a.
d.
no point of intersection
x+2 y-3 z-2
49. Determine the parametric equation of the plane that contains the line
5
and the point
2
%3D
%3D
3
P(2,5,3).
a. x = 2+ 5s + 4t, y = 5 + 3s + 2t, z = 3 + 2s + t, s,t e R
b. x = 2+ 5s + 3t, y = 5 +3s + 2t, z = 4 + 2s + t, s,t e R
c. x = -2+5s +2t, y = 3+3s + 5t, z = 2+ 2s + 3t, s,t e R
d. x = 5+2s + 2t, y = 3– 3s + 5t, z = 2 – 2s + 3t, s,t e R

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