Winter 2022 | Calculus & Vectors | Grade 12 Unit 6 Test - Introduction to Vectors Knowledge & Understanding Communication Thinking & Inquiry Application 16 12 /13 /18 Knowledge & Understanding 1 Which expression is meaningless? [K /1] a. axb x c b. (axb ) . c c. (axb) . c d. (a - b) . c e. a . (b x c ) 2. The vector result of (1 - 2] + 3k) X(-21 + 2] - 2k) is [K /1] a. -i+ 7j b . -it j -k C. -7- J+ 3k d. j+ 7k e. -i+ 7k 3. The result of the following dot product (1 - 2j + 3k) . (-21 + 2J - 2k) is [K /1] a. -10 -6 C. 0 d. 10 6 4. Which relation is incorrect: [K /1] a. i . j = 0 b. ix j = k c. ixi= 0 d. j. k = i e. 1. i = 15. A vector collinear to u = is: a. [K /1] b. d. C. e. 6. If u = and v = and u is orthogonal to v, then k is [K /1] a. -8 8 . 4.5 d. -4.5 e . 0 7 Which property of vectors is incorrect? [K /1] a. axb = -bx a b. (atb) + c= a+ (b+ c) c. a . (b + c ) = a+ (b+ c ) d. a . b = axb 8 Which vector is not orthogonal to u =? [K /11 a. b. C. d. 9 Given A(1, 3, -7) and B(0, 2, -4), the magnitude of AB is [K /1] a. V147 b. 3 C. VII d. 3.310. Vectors a, b, c are given below. Accurately draw the following vectors. [K /41 a. u = 3a - b + 0.5c [2] b. D = =b - 2a + c [2] C Applications 11. Consider the following vectors a = 2i + 3j and b = -21 + 3k and c = -31 + k Compute the required operations: [A /10] a . 4a . 2b [2] c. (axb) . c [2] b . la + ( b x c ) I [2] d. projc(a - b) e. [2] Angle between a and c [21Thinking & Inquiry 14. [4] List as many equal vectors as possible for the diagram below: B E 15. [4] A ramp is inclined at 120 to the horizontal. A cart is pulled 8 m up the ramp by a force of 120 N, at an angle of 10 to the surface of the ramp. Determine the mechanical work done against gravity. 16. [4] A parallelogram has an area of 200 cm2. The side lengths are 90 cm and 30 cm. Find the measures of the interior angles.Communication 2 13. [6] Describe all of the operations involved in (a . b) (a . c) - 2a . (b x c) Explain whether the final result will be a scalar or a vector.12. Consider parallelogram ABCD where A(0, 1, 2), B(1, -2, 3), D(2, 1, 0) [A 18] a. Find angle LA [2] b. Find the area of triangle AABD [3] C. Find the angle between the diagonal AC and the side AB [3]