Find a vector parametrization of the line through P = (0, -3, -2) in the direction V = (6, 4, 1) r(t) = ( 1 1 + + - t) j+ t) k t) i+ I +

Q: = (4, 1, a), Q = (–2, 0, b) and v = i – 3j + 4k be two points and a vector in R³ respectively. (a)…

A:

Q: Determine a vector equation for hte line through the point: (-2, 0, -8) perpendicular ot the plane:…

A:

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

A:

Q: Find a vector orthogonal to the line x+y=1

A:

Q: Find a vector parametrization of the line through P = (3, -5, 7) in the direction v = (3, 0, 1)

A: Given:P=3,-5,7v=3,0,1

Q: Find the intersection of the line that passes through (0,3,-1), in the direction of…

A:

Q: Let V1 = 2 V2 = 0 2 V3 = 2 V4 = 3 Decide the dependence or independence of the vectors {V₁, V2, V₁}…

A:

Q: Where does the line with the vector equation [x,y,z] = [6, 7, -8] + t[-2, 4, 1] intersect the…

A:

Q: 1 Consider the line through the vector a = Find the project of b = (1,2,3) onto this line.

A:

Q: Find the equation of the plane P spanned by vectors  v = (2,1, 3)  and w = (1,2,-1)  containing the…

A: The given problem is to find the equation of plane P that is spanned by given two vectors and…

Q: The velocity vector of a particle in the xy-plane is (√7, 9e³-3) for all real t. If the position of…

A: The velocity vector in the xy-plane is for all real t. If the position of theparticle at , then to…

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

A:

Q: Find the projection of v = [-3, 3, 6] onto the line L with vector equation x=td where d = [4, -3, 1]

A: