Find a vector parametric equation F(t) for the line through the points P = (5,-5, -5) and Q = (10, -6, -9) for each of the given conditions on the parameter t. (a) If 7(0) = (5, -5, −5) and 7(8) = (10, -6, -9), then r(t) = (b) If 7 (5) = P and 7(9) = Q, then F(t) = (c) If the points P and Q correspond to the parameter values t = 0 and t= -2, respectively, then F(t) =

Q: 4. Write the vector equation for a line parallel to the line L: F = (1,-7)+t(2, -3), t € R…

A: Introduction: In three-dimensional geometry, a line can also be described through a vector equation,…

Q: X = Find the vector equation for the line of intersection of the planes x − 5y + 5z = −5 and x + 5z…

A: Given the equation of planes x-5y+5z=-5 and x+5z=1. To find the vector equation for the line of…

Q: A vector equation for the line through the points A (3, -4, -3) and B (3,4,2) is (x, y, z) = . (You…

A: Concept to be used:If a line passes through two points A,Bwith position vectors aand brespectively,…

Q: Find a vector equation for the line through the point (4, 5, -1) perpendicular to the vectors , 6,…

A: we have to find the line equation passing through point (4,5,-1) and perpendicular to the vectors…

Q: The vector parametric equation for the line through the points (-3, 5, −4) and (5, −5, 0) is L(t) =

A: The given points are -3, 5, -4 and 5, -5, 0. We have to find a parametric equation.

Q: (a) Determine the vector and parametric equations of the line containing points E (-1, 5) and F (6,…

A:

Q: Let L₂ be the line passing through the point P₁=(-3, -1, -2) with direction vector -[0, 3, 3], and…

A:

Q: Find both the vector equation and the parametric equations of the line through (-3,3,7) and (3, -…

A: Consider the points <-3,3,7> and <3,-1,0>. The vector equation and the parametric…

Q: Let Lz be the line passing through the point P-(10, 1. –10) with direction vector d--2, -2, 3]", and…

A: We will use formula for the shortest distance.

Q: Find the vector and parametric equations for the line through the point P(-2, 1, -5) and the point…

A:

Q: o find the image of v and the preimage of w. , 2vq – v2 ), v = (1, 1), w = (-7/7, 2, -20) age of v…

A:

Q: Find a vector equation for the line through the point P = (-3, 5, -4) and parallel to the vector v =…

A:

Q: Find an equation of the plane orthogonal to the line which passes through the point (-9, 10, -6).…

A: given equation of orthogonal line

Q: Let Lz be the line passing through the points Q1=(1, 3, 1) and Q2=(7, 12, 4). Find a value of k so…

A: We will solve the problem

Q: Suppose the straight lines L₁ and L2 have respective vector equations 5 4 r1 = -3 + t 3 where s and…

A: