Note: all vectors are diplayed vertically.

1)

a) Find det(A)
b) Find adj(A)
c) Using (a) and (b), find A^-1
d) Use Cramer's Rule to solve AX =

(10)

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2) u = , v = , w = . Compute the following:

a) 2(u + w) - v	b) 7(u + 2v) - 6w	c) É u + v É
d) h if h is the angle between u and v	e) Area of the parallelogram defined by v and w
f) projv u

(15)

3) u = , v = ,

a) Find w such that w is parallel to u and || w || = 1.

b) Find x such that x is perpendicular to u and v.

c) Find y such that 2u - 3v = y.

d) Prove that u is not orthogonal to v.

e) Evaluate 3u $ (u - 2v)

(10)

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4) a) Write the parametric equations of the line through P(-1, 2, 1) parallel to u =

b) Write the equation of the plane through P(1, 1, 2), Q(0, 2, 3) and R(-1, -1, -4).

c) Write the parametric equations of the line of intersection of the planes
x + y + z = 0 and x + y = 1.

d) Find the intersection points of the plane 3x + 2y - z = 10 and the line .

e) Find all points of intersection (if any) of the lines l₁ : , l₂ :

f) Prove that the line is parallel to the plane 2x + y - 9z = 12.

(15)

TOTAL (50)

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