Suppose f(x, y) = (1, -3). Then, (a) Vf(x, y) = (b) Vƒ(1,5) = (c) fu (1,5) = Du f(1,5) = x² + y² and u is the unit vector in the direction of

Find the vector equation of a line L going through the point P = (-5, -6) and parallel to the line generated by multiples of the vector v = --HA 1 L(t) - +t

Explain how to find a vector in the direction of the line segment from P0(x0, y0, z0) to P1(x1, y1, z1).

Draw the vectors in standard position in R2 with their tails at the point (2, -3).

Suppose f(x, y) = (a) ▼ f(x, y) = (b) Vƒ(-0.7, 7) = tan(x) + y and u is the unit vector in the direction of (2, 3). Then, (c) fu (−0.7, 7) = Du f(−0.7, 7) = ← ▶ ←

Suppose f(x, y) (a) ▼ ƒ(x, y): = (b) ▼ƒ(1,4) = = = 0 2 x² + y² and u is the unit vector in the direction of (2, -1). Then, Your answer should be a vector Your answer should be a vector (c) fu (1, 4) = Du f(1,4) = = Your answer should be a number

2. (a) (b) (c) Determine if the vectors are linearly independent. Justify your answer. [B] HI 22 and and " and ان ان -3 3

Find the coordinates of a point P on the line and a vector v parallel to the line x = 3 - 5t, y = -1 + 2t, z = -2 O P(3,-1, -2), v = (-5,2,0) O P(-5,2,0), v = (3, 1, 2) O P(-3, 1, 2), v = (5,-2, 0) OP(5,-2, 0), v = (-3, 1, - 2)

Let v = (2, 4) and w = (3,-5) (a) Find a vector of unit length in the same direction as w. (b) Find ✓ – 2w and write your answer in terms of the unit vectors ỉ and j. (c) Find scalars a and b so that av + bw = (8,-17).

Find the vector equation of the line(a) through the point (1, −5) and parallel to the x-axis;(b) through (2, 1) and (−3, 8);(c) through the point (2, −8) and with gradient −4/5;(d) through (6, −3) and parallel to the line through (5, −1) and(2, 11);(e) through (1, −1) and parallel to the median from A of thetriangle A(2, 3), B(6, 1), C(7, 3).