assignment1 - MATH 1300 ASSIGNMENT PROBLEMS(UNIT 1[10 1 AOB...

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MATH 1300 ASSIGNMENT PROBLEMS (UNIT 1) [10] 1. AOB is the diameter of a circle with centre at O and C is any other point on the circle. Denote the vector OAby a and the vector OCby (a) Write the vectors ACand CBas linear combinations of the vectors a and (b) Use vector methods to show that ACBis a right angle. [10] 2. Let A = (2, 1, 5) and B = (1, 2, 4) be two points in (a) Find the components of the vectors ABand BA(b) Find the coordinates of the point C if ACCB(c) The point D = (k, 1, 5) is equidistant from the points A and B. Find the value(s) of (d) Find the coordinates of the point X for which AX2AB[10] 3. Let (4,3,1),(5,4,2) and (7, 3,4)uvwbe three vectors in R3. Find the following. (a) 23uv(b) u v(c) v(d) projv(e) sine of the angle between the vectors uand A C a c O c. c. R3. . . k. . wuuv. B
[10] 4. Let u= (4, 2, 7) and v= (2, 1, k) be two vectors in (a) For what value(s) of kwill the two vectors R3.

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