Vector Addition and Subtraction In general it is best to conceptualize vectors a

Question

Vector Addition and Subtraction In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components. Let vectors A = (1,0,-3). B = (-2,5,1), and C = (3,1,1). Calculate the following, and express your answers as ordered triplets of values separated by commas Part A ANSWER: A-B = 3,5,4 Correct Part B ANSWER: B-C= -5,4,0 Correct Part C ANSWER: Part D ANSWER: 3A-20. 3A-2C = Part E ANSWER: -2A + 3B-C= Part F ANSWER: 2A- 3(B -C)

Explanation / Answer

best method for vector addition or subraction is to do the process component wise.

i.e. if addition is to done, add x component of one vector with the x component of the other vector and so on.

similarly for subtraction too.

part A:

A-B=(1,0,-3)-(-2,5,1)

=(1-(-2), 0-5, -3-1)

=(3,-5,-4)

part B:

B-C

=(-2,5,1)-(3,1,1)

=(-2-3, 5-1, 1-1)

=(-5,4,0)

part C:

-A + B - C

=-(1,0,-3) + (-2,5,1) - (3,1,1)

=(-1-2-3, 0+5-1, 3+1-1)

=(-6,4,3)

part D:
3A-2C
=3*(1,0,-3)-2*(3,1,1)

=(3,0,-9)-(6,2,2)

=(3-6,0-2,-9-2)

=(-3,-2,-11)

part E:

-2A+3B-C

=-2*(1,0,-3)+3*(-2,5,1)-(3,1,1)

=(-2,0,6)+(-6,15,3)-(3,1,1)

=(-2-6-3,0+15-1,6+3-1)

=(-11,14,8)

part F:
2A-3*(B-C)

=2*(1,0,-3)-3*(-2-3, 5-1,1-1)

=(2,0,-6)-3*(-5,4,0)

=(2,0,-6)+(15,-12,0)

=(17,-12,-6)

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