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).

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)