# Vector operations

Express the vectgor with initial point P and terminal point Q in component form. Show work.

12. P(1,1), Q(9,9)

14. P(-1,3), Q(-6,-1)

16. P(-8, -6), Q(-1, -1)

Find 2u, -3v, u + v, and 3u - 4v for the given vectors u and v. Show work.

18. u= (-2,5), v= (2, -8)

20. u= i, v=-2j

Find (a) u * 5 and (b) the angle between u and v to the nearest degree.Show work.

2. u = i + sqaure root of 3j, v= -square root3i + j

4. u= (-6,6), v=(1, -1)

6. u= 2i + j, v= 3i-2j

8. u= i + j, v= i-j

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#### Solution Preview

Express the vector with initial point P and terminal point Q in component form. Show work.

12. P(1,1), Q(9,9)

Solution. Given the initial point P(x1,y1) and terminal point Q(x2, y2). Then the vector

PQ=(x2-x1, y2-y1)

In this question, x1=y1=1, x2=y2=9. So,

PQ=( x2-x1, y2-y1) = (8, 8)

14. P(-1,3), Q(-6,-1)

Solution. Given the initial point P(x1,y1) and terminal point Q(x2, y2). Then the vector

PQ=(x2-x1, y2-y1)

In this question, x1=-1, y1=3, x2=-6, y2=-1. So,

PQ=( x2-x1, y2-y1)

=(-6-(-1), -1-3)

= (-5, -4)

16. P(-8, -6), Q(-1, -1)

Solution. Given the initial point P(x1,y1) and terminal ...

#### Solution Summary

The solutions consist of details of all kinds of vector operations.