The direction angles of a nonzero vector a are the angles a, ß, and y (in the interval [0, m]) that a makes with the positive x-, y- and z- axes, respectively. The cosines of these direction angles, cos(a), cos(B) and cos(y), are called the direction cosines of the vector a. For a vector a = (a, b, c), the direction cosines are given by cos (8) cos(a)= cos(B)- Find the direction cosines and direction angles of the vector (5, 1, 3). (Give the direction angles correct to the nearest degree.) ▷ lal lil cos(y) - a= B= Y= D cos(a) 0 lal lal lil cos(y) = a k la |k| lal

Q: Given the vectors w = and z = , find the results of the vector subtractions. -W-Z= Z-W= W-Z=

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Q: Let ú = (0, – 3, 2) and i = (5, 0, – 5). (a) Find i - v: i - v = (b) Find the angle 0 between the…

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Q: (a) Let a = (−1, 4, 2, 1), b = (0, 2, 2, 0), c = (-1, 3, 4, 0), d = (-2, 9, 8, 1), and U(a, b, c, d)…

A: Step 1: Step 2: Step 3:Step 4:

Q: Given vector u= (-3, 3) and v = (6, –2), determine the value of 4u + v in | component form.

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Q: 6.) For each position vector given, (a) graph the vector and name the quadrant, (b) compute its…

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Q: Given u = and v = , sketch u - 2v and identify the direction (from standard position a.k.a. (+)…

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Q: Consider vectors u = (4, 1) and V = (-1, 3). a. Find the linear combination W = 2u - 3v. b. Find the…

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Q: Let v be a nonzero vector. The angles a, ß, y between v and the unit vectors i, j, k are called the…

A: Express the vector v in terms of i , j and k and find the values for direction cosines.…

Q: Given vector u = (-3,2) and v = (-3, –1) , determine the value of v – 2u ir component form.

A: We can determine the component form as below.

Q: Given the points A: (-6,6,-5) and B: (3,-1,0), find the vector i AB i = <

A: Since, we have been given the points A (-6,-6, 5) and B(3,-1, 0).Our Aim is to find the vector u⇀…

Q: 2. Find the position vector v for each of the following pairs of points. Point P is the initial…

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