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)
