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- Question : 1R - Mark each of the following statements true or false: (a) For vectors U, v, and w in rr;r, if u + w = v + w, then u = v. (b) For vectors U, v, and w in rr;r, if u . w = v . w, then u=v. (c) For vectors u, v, and w in IR 3 , if u is orthogonal to v, and v is orthogonal to w, then u is orthogonal to w. (d) In IR 3 , if a line C is parallel to a plane <:IP, then a direction vector d for e is parallel to a normal vector n for <:IP. (e) In IR 3 , if a line e is perpendicular to a plane <:IP, then a direction vector d for e is a parallel to a normal vector n for <:IP. (f) In IR 3 , if two planes are not parallel, then they must intersect in a line. (g) In IR 3 , if two lines are not parallel, then they must intersect in a point. (h) If v is a binary vector such that v
- Question : 2R - If u = [ -? l v = [ ? l and the vector 4u + v is drawn with its tail at the point ( 10, - 10), find the coordinates of the point at the head of 4u + v.
- Question : 3R - If u = [ -?l v = [?l and 2x + u = 3(x - v), solve for x.
- Question : 4R - Let A, B, C, and D be the vertices of a square centered ----> at the origin 0, labeled in clockwise order. If a = OA and b = OB, find BC in terms of a and b.
- Question : 5R - Find the angle between the vectors [ - 1, 1, 2] and [2, 1, - 1].
- Question : 6R - Hnd ilie prnjection of v ? [:] onto u ? [ -n
- Question : 7R - Find a unit vector in the xy-plane that is orthogonal tom
- Question : 8R - Find the general equation of the plane through the point ( 1, 1, 1) that is perpendicular to the line with parametric equations x = 2 - t y = 3 + 2t z = -1 + t
- Question : 9R - Find the general equation of the plane through the point (3, 2, 5) that is parallel to the plane whose general equation is 2x + 3y - z = 0.
- Question : 10R - Find the general equation of the plane through the points A(l, 1, O), B(l, 0, 1), and C(O, 1, 2).
- Question : 11R - Find the area of the triangle with vertices A(l, 1, O), B(l, 0, 1), and C(O, 1, 2).
- Question : 12R - Find the midpoint of the line segment between A = (5, 1, - 2) and B = (3, - 7, 0).
- Question : 13R - Why are there no vectors u and v in !Rn such that ll u ll = 2, llv ll = 3, and u
- Question : 14R - Find the distance from the point (3, 2, 5) to the plane whose general equation is 2x + 3y - z = 0.
- Question : 15R - Find the distance from the point (3, 2, 5) to the line with parametric equations x = t, y = 1 + t, z = 2 + t.
- Question : 16R - Compute 3 - (2 + 4)3 (4 + 3)2 in Z5.
- Question : 17R - If possible, solve 3(x + 2) = 5 in Z7
- Question : 18R - If possible, solve 3(x + 2) = 5 in Z9
- Question : 19R - Compute [2, 1, 3, 3]
- Question : 20R - Let u = [l, 1, 1, O] in Zi. How many binary vectors v satisfy u

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