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Find a vector ū with |||| = 2758 that has the opposite direction to ū= -31...
Find a unit vector in the direction ū if ū is the vector from P(2,1, -3) to ((-1,0,4). Then, find c such that vector PR is orthogonal to ū where Ręc, c,c).
11. (8 marks) Given the vector ū = (3,-2, -5) (a) Find the unit vector with direction opposite to ū (b) Find the vector component of ū orthogonal to ū = (-1,2, -3)
1. Given the vectors ū=(1,-2,-6) and v = (0,-3,4), a) Find u 6v. b) Find a unit vector in the opposite direction to ū. c) Find (ü.v)v. d) Find 11: e) Find the distance between ū and v. f) Are ū and y parallel, perpendicular, or neither? Explain. g) Verify the Triangle Inequality for ū and ū.
006 10.0 points Find the vector ✓ with magnitude 3 and the same direction as ū= (4, -4). 1. (3,-3) wios 12' 2) 4. None of these
1) Find a vector of magnitude 9 in the direction opposite to the direction of 8 = și + -
9. [6 pts) Find a vector of length 15 in the opposite direction of the vector v = (-7,24).
Consider the vector v = (14, 14, 4). Find u such that the following is true. he vector u has the same direction as v and one-half its length. u = (b) The vector u has the direction opposite that of v and one-fourth its length. U = (c) The vector u has the direction opposite that of v and twice its length. U =
13 2. Find a vector i of length 3 in the direction of a = [1,2,3]. 3. Consider the vectors th=[k, 2, -11) and (a) ū and are perpendicular. [3] (8.k, 1). Find the possible values of k such that: (b) u and ū are parallel. Sand ğ vectors in Rº such that P+q1l = 2 and P-911 = 3. Find p.7.
2. Let ū= (3,1, -7), ã = (1,0,5). (a) Find the vector component of u along a. (b) Find the vector component of ü orthogonal to ä. (c) Find the angle between u and , in degrees.
3. If ū= 4.2,1 and ū= -2.2.1), find a vector in R3 that is orthogonal to both ū and . Answer: 4. Let A, B and C respectively denote the points (1,1,2), (-3, 2, 1) and (4, -2, -1). Find AB, AC and AB X AC. Answer: AB= AC = 1. AB X AC = 5. (a) Find the equation of the plane containing the points A, B and C above. Answer: (b) Check that your answer to (a) above...