Chapter 11.5, Problem 62ES

Find a parametric equation of the line passing through the point(3,-1,-3) and perpendicular to the line joining (3,-2,4) and (0,3,5) . (this is a question of linear algebra)

How do you subtract two vectors algebraically? Geometrically?

write v in form ai+bj, find its position vector. There are 2 examples I need to find and solve: example I:          P=(3,2); Q=(5,6) example II:          P=(1,0); Q=(0,1)

Describe the graph of the equation: r = 3i – 5j + (1 + 30)k. [Choose the correct answer.] O The equation is a line in 3-space through the point (3) and parallel to the vector - 5j + k. O The equation is a line in 3-space through the point (0, - 5) and perpendicular to the vector 3i + 3k. O The equation is a line in 3-space through the polnt (0, – 5) and parallel to the vector 3i + 3k. O The equation is a helix in 3-space containing the point (0, – 5) and above a circle with radius 6.

Find an equation of the plane passing through the points (-1,2,0), (2, 3, 6), and (-1, 0, 2). Use vector operations only.

A rocket ship in space is not moving. The ship's crew performs a rocket burn which can be described by the vector components (-22,-31). The astronauts make a second burn that can be described by the components (22,-80). The astronauts make a final burn that can be described by the components (31,60) a. What are the components of the vector that describe the accumulation of the three maneuvers? explain. b. What does this vector represent? Explain. c. What are the components of the vector would negate all of the other burns? Explain.