Assigned Week 4 Block 11 by Dr. Rickert. Due by 5PM Tuesday, October 5.

Problem 1

Find the size and direction of the vector 7 i + 5 j .

> with(linalg):

> v1 := vector([7,5]):

size (magnitude) is equal to the square root of the dotproduct of itself

> v1m := sqrt(dotprod(v1,v1));

direction is equal to the unit vector

> evalm(v1/v1m);

Problem 2

Find two vectors that are parallel to the vector 10 i + 20 j .
Be sure to explain how you know that they are parallel.

> v2 := vector([10,20]):

> evalm(v2*2);

> evalm(v2*5);

these vectors are parallel because the slopes are the same as the original vector, as determined by y/x

Problem 3

Find a vector that is perpendicular to the vector 5 i + 8 j .
Be sure to explain how you know that it is perpendicular.

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Problem 4

Problem 5

Problem 6

Problem 7

Problem 8