Solve the problem.
1) Find the area of the parallelogram determined by the points P(7, -5, 5), Q(-10, 8, -7), R(-4, -5, 1)and
S(-21, 8, -11).
A) 3 7017 B) 3 7017
2 C) 27249 D) 27249
2
Find the triple scalar product (u x v) · w of the given vectors.
2) u = 2i – 4j + 3k; v = -3i – 5j + 2k; w =8i -6j +10k
A) 66 B) -86 C) -246 D) 282
Find parametric equations for the line described below.
3) The line through the points P(-1, -1, -2) and Q(-4, -7, 1)
A) x = t – 3, y = t – 6, z = -2t + 3 B) x =-3t -1, y =-6t – 1, z = 3t – 2
C) x = -3t + 1, y = -6t + 1, z = 3t + 2 D) x =t +3, y =t +6, z = -2t – 3
Write the equation for the plane.
4) The plane through the point P(-3, 5, 7) and normal to n =7i +5j +4k.
A) 7x + 5y + 4z = 32 B) -3x +5y +7z =32 C) -7x -5y -4z =32 D) 3x -5y -7z =32
5) The plane through the points P(-1, 3, -15) , Q(2, -1, 14) and R(1, 5, -19).
A) 3x + 5y +z = 3 B) 3x +5y +z =-3 C) 3x -5y -z =-3 D) 3x -5y -z =3
6) The plane through the point P(2, -8, -3) and perpendicular to the line x =9+9t, y = 4 + 3t, z =8+8t
A) 9x + 3y + 8z = -9 B) 9x +3y +8z =20 C) 9x +3y +8z =-30 D) 9x +3y +8z =30
Calculate the requested distance.
7) The distance from the point S(-6, -8, -4) to the line x =-10+2t, y =6+9t, z = 4 + 6t
A) 4 365
11 B) 4 365
121 C) 5840
121 D) 5840
11
8) The distance from the point S(9, -7, 7) to the plane 11x +10y +2z =6
A) 37
225 B) 7
75 C) 7
5 D) 37
15
Find the angle between the planes.
9) 9x + 10y + 7z = -6 and 2x + 7y + 7z = 2
A) 0.464 B) 1.400 C) 1.107 D) 0.851
Find the intersection.
10) x = 2 + 2t, y = -8 + 9t, z = -3 + 3t ; 10x +2y +4z =10
A) (0, -17, -6) B) 68
25, -119
25 , -48
25 C) 32
25, – 146
25 ,- 2
25 D) (4, 1, 0)
