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MA 126 Test 1 NAME___________________________
100 points Spring, 2010
PART 1. Part 1 consists of 6 questions. Show your work and clearly mark your final answer in the
space provided. (5 points each)
- Given the vector a =< 5, −3, 2 >,
find a unit vector in the direction of a
- Find the equation of the line through the points P ( 2,0,1)− and Q (2,1, 2).
- Find a vector perpendicular to both of the vectors a =< 1,0,1>
and b = < 0, −1, 2 >
- Let a =< 1, −1,3 >
and b = < 0, −1, 2 >
. Find the scalar projection compb ^ ( ) a
and vector projection
projb ^ ( ) a
of a
onto b
- Find the angle between the vectors a = < 1, −2, 2 >
and b = < −1, 2,3 >
. (You may leave your answer
in the form
1 θ cos ( ) x
− = .)
- Find the equation of the plane through the point ( 1, 2,3)− which is perpendicular to the line
x t
L y t
z t
^ = −^ +
3 Find the parametric equations for the tangent line to the helix given below at the point P where
where 2
t = π.
x = 2cos( ), t y = sin( ), t z = t
- Find a vector equation or parametric equations for the line of intersection of the planes
2 x + y + z = 1 and x + 2 y = 7.
- Find the distance from the point ( 1, 2,3)− and the plane 2 x − y + z = 5.
- Given the two lines 1 2
1
x t
L y t
z t
^ =
and (^2)
x s
L y s
z s
^ =^ +
. determine if they are
parallel, skew, or intersect. If they are parallel, determine if they are identical lines. If they intersect, determine the point of intersection. If they are skew, find the distance between the lines.
