# Find the volume and surface area of the parallelepiped having adjacent edges defined by A(1, 2, 5), B(4, 8, 1), C( — 3, 2, 3), D(0, 3, 9).

Linear Algebra

Part I: Say TRUE or FALSE in the space provided [Each worth 1pt.]

1. Vector is a physical quantity that is described by its direction.

2. For any two vectors ii = u2) and .147 = (v1, v2) in 118z , u = v if u1 = v1 and u2

3. Any column and row matrices are vectors

4. Located vector is a vector whose initial point is at the origin.

5. The vector 0 is parallel to every vector v in the same dimension.

6. W/ T3 if there exists a scalar c such thatV = c v.

Part II: Choose the best answer and encircle your choice [Each worth 1pt.]

7. The vector PiPz if the points PI and P2 are given by P1(4, 6, — 2) and P2(1, 8, 3).

A. (3, — B. (— C. ( — 3,2,5) 2, — 5) 3,2, — 5) 8. The norm of a vector v = 4, 6 ) is
A.7
C. -1
= v2..1
D. None

B. A unit vector D. None

9. The angle between the vectors u = i and v = i + k in He —2 A. B. 7 C. 7r D. None

10. The value of x and y so that v = (x, y, 1) is orthogonal to both vectors a = (3, 1, — 1 ) and V = (- 3, 2, 2 ) A. x = 1/9, and y =— 1/3. C. x =— 1/9, and y =— 1/3 B. x = 1/9, and y = 1/3 D. None

Part III: Workout [Show all the necessary steps clearly and logically at the back side of the question Paper]

11. Given two vectors u = 3i — 4j and v = 2i — j in II83 then determine
(lpoint each)

a) u. v

b) Ilu x vii

c) A unit vector in the direction of u x v

d) Prop,’

12. Find the area of the triangle with vertices A(1, 2, 1), B( — 3, 4, 6), and C(1, 8, 3).

13. Find the volume and surface area of the parallelepiped having adjacent edges defined by A(1, 2, 5), B(4, 8, 1), C( — 3, 2, 3), D(0, 3, 9).
(3 point)
(3 point)

Find the volume and surface area of the parallelepiped having adjacent edges defined by A(1, 2, 5), B(4, 8, 1), C( — 3, 2, 3), D(0, 3, 9).