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=

A:

Q: In the picture below, x = (*) and (3). V= 7 u = The vectors p and r are also shown in the picture,…

A:

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

A:

Q: 3

A:

Q: Again referring to the vectors a = (5,3,7) and b = (2,-3,4), a. What is the angle between them? b.…

A:

Q: Let a = (5, – 4, – 2) and b = (0, – 2, 3). Find the angle between the vector (in radians)

A:

Q: Let v =. Find the unit vector in the opposite direction of v.

A:

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

A:

Q: 6. Evaluate (9-4x2) dx

A: We need to use Trigonometry substitution to solve this integration  and we use formula  2cos2x =…

Q: Let å = (0, 3, – 5) and 6 = (3, 1, – 3). Find the angle between the vector (in radians)

A:

Q: Define the points P = (-4, 6) and Q = (2, 4). Find the position vector corresponding to På. %3D %3D…

A: We will find the position vector of PQ as following

Q: The direction angle y of the vector (1,1,1) is 45° Cos-¹) 60° 30° BO .CO .D O

A:

Q: Find the direction angle of the vector u=

A:

Q: Find the component form of the vector 1 The vector PG where. På PC1,3) and Q5 (2₁-1). The vector…

A: To find the component form of the vector.(1) The vector (2) The vector from the point  to the…

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: Let P be the point (1, –3, 0) and ū be the vector ī = (-3, 6, 2) %3D • Find the point 1 unit away…

A: Given: The point P=(1,-3,0) and the vector v→=-3,6,2

Q: Find the direction angle 0 of the vector v = .

A:

Q: Draw position vector OP = (-2,-4,3) on the axis below.

A:

Q: .4 Find the angle between the position vectors to the points (3,-4,0) and (-2, 1, 0) and find the…

A:

Q: 7.(a) A and Care the points (1,3, –2) and (4,–4,4) respectively. Point B divides AC in the ratio…

A: We find a coordinate in given ratio.