MATH 215 MID TERM EXAM
EQUATIONS/TERMS EXAM
QUESTIONS AND ANSWERS 2026
Distance Formula - ANSWERSsqrt((a2-a1)^2 + (b2-b1)^2 + (c2-c1)^2)
scalar x vector = - ANSWERSvector
unit vector equation - ANSWERSu = (1/ mag of a) x a
finding the angle between vectors - ANSWERSa dot b = (mag of a) x (mag of b) x
cos(theta)
2 vectors are perpendicular/orthogonal if... - ANSWERSdot product of the 2 vectors is 0
vector projection of b onto a (proj a ^b) - ANSWERS((a dot b)/(magnitude of a)^2) x a,
projections are vectors
component of b onto a (comp a ^b) - ANSWERS(a dot b)/a, components are scalar
Cross Product - ANSWERS(a2b3-a3b2)i -(a1b3-a3b1)j + (a1b2-a2b1)k
To show (a cross b) perpendicular to a - ANSWERS(a cross b) dot a = 0
Area of triangle - ANSWERS(1/2) times (magnitude of vector 1 cross vector 2)
Find a vector perpendicular to plane passing thru 2 vectors - ANSWERScross the 2
vectors
Line - ANSWERSa line in 3D is determined by a point P(x,y,z) on L and a direction of
Line l
vector equation of a line - ANSWERSr = r + tv
Parametric equations - ANSWERSEx: x = x0 + at
Find the vector and parametric equations for the line passing through (1,-2,8) and
parallel to 2i + 3j - k. - ANSWERSVector Equation: <1 + 2t, -2 +3t, 8 -t>
Parametric Equation: x = 1 +2t, y = -2 +3t, z = 8 -t
To find more points on a line - ANSWERSplug in values for t in the vector or parametric
equations
EQUATIONS/TERMS EXAM
QUESTIONS AND ANSWERS 2026
Distance Formula - ANSWERSsqrt((a2-a1)^2 + (b2-b1)^2 + (c2-c1)^2)
scalar x vector = - ANSWERSvector
unit vector equation - ANSWERSu = (1/ mag of a) x a
finding the angle between vectors - ANSWERSa dot b = (mag of a) x (mag of b) x
cos(theta)
2 vectors are perpendicular/orthogonal if... - ANSWERSdot product of the 2 vectors is 0
vector projection of b onto a (proj a ^b) - ANSWERS((a dot b)/(magnitude of a)^2) x a,
projections are vectors
component of b onto a (comp a ^b) - ANSWERS(a dot b)/a, components are scalar
Cross Product - ANSWERS(a2b3-a3b2)i -(a1b3-a3b1)j + (a1b2-a2b1)k
To show (a cross b) perpendicular to a - ANSWERS(a cross b) dot a = 0
Area of triangle - ANSWERS(1/2) times (magnitude of vector 1 cross vector 2)
Find a vector perpendicular to plane passing thru 2 vectors - ANSWERScross the 2
vectors
Line - ANSWERSa line in 3D is determined by a point P(x,y,z) on L and a direction of
Line l
vector equation of a line - ANSWERSr = r + tv
Parametric equations - ANSWERSEx: x = x0 + at
Find the vector and parametric equations for the line passing through (1,-2,8) and
parallel to 2i + 3j - k. - ANSWERSVector Equation: <1 + 2t, -2 +3t, 8 -t>
Parametric Equation: x = 1 +2t, y = -2 +3t, z = 8 -t
To find more points on a line - ANSWERSplug in values for t in the vector or parametric
equations
