13 2. Find a vector i of length 3 in the direction of a = [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.
9. Find the component form of the vector that starts at (3,-2) and ends at (-1,9). 10. If the terminal point of vis (4.7) and v = Ti - 13), find the initial point of v. 11. Find a imit vector in the same direction as 211 - 7. 12. Determine whether V and w are parallel. orthogonal, or neither. B. v= -2i+3j, w = -6i+9j A. V = 3i-57. w = 6i - 103 18 C. v = 3i...
Question 17 Find the vector v with length 3 and the same direction as the vector u =(-1,6,5). •-( tas var - to vote --( tez le ton) Question 18 Find the angle in radians between the vectors u = (0,6, 0,6) and v- (3,5,6,3). Round your answers to three decimal places 1.224 radians 1.003 radians 0.297 radians 0.995 radians 0.881 radians
#2 show work 2. (5 points) Find a vector of length 3 that is perpendicular to the line given by -3x + 7y = 11. Express the result in terms of the unit vectors i and j. 3. (10 points) A truck is parked on a driveway inclined 19° to the horizontal. A force of magni- tude 920 pounds is required to keep the truck from rolling down the driveway. a. Find the vector representing this force and express it...
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) The displacement vector A las a length La and a direction east of north; the displacement vector B has a length Le and a direction west of north. What are the magnitude and direction of Ax B? (b) B x A? (c) Write out the vector A x B in terms of the unit vectors i, j, and k. [15 pts] (2) A boat with a maximum speed v (relative to the water) is on one shore of a...
7. Find the angle between the vectors. ü = (-3,2) and v = (-1,1) e perpendicular. 112 - at 4. Find the vector v such that. ||3|| = 9 and having the same direction as ū. ū=(3,-2)
Let's examine the following vectors: ūj = (6,8), ū2 = (5,6) ū = (4, 2, 4) ñ 1 = (7, 3, 1, 3) ja W2 = (7,5, 1, 10). 1. Define vector norms, i.e. lengths. 2. Specify a vector of length 1 and which is parallel to the vector v 3. Find a vector that is perpendicular to the vector Új
1. u Test s. = <1,2,2>. Point p (-1,0,2). Find (1), the direction cosines of u 12. the live through point p that's perpendicular to ū and parallel to the place 2x-y +38=7 2. Name and sketch the graph for the equation 4x²+y²-28 -8x + 2y +8=0.