2 Let I be the line in R³ that consists of all scalar multiples of the vector w = -[] 2 Find the reflection of the vector v = reflection = [8] 8 in the line L.

Q: Let L₁ be the line passing through the points Q₁-(-1.-3, 1) and Q₂-(-4,-6, 2). Find a value of k so…

A:

Q: Let L. be the line passing through the point P=(5, 1, 1) with direction vector [-1,5, -2], and let T…

A: Solution :

Q: Compute the orthogonal projection of v= 7 onto the line through 4 2 and the origin.

A:

Q: Q5) the value of the constant a for which the line x=2+t,y=2+3t,z=3+t and the plane ax+y-2z-7=0 are…

A: We will use definition.

Q: Compute the orthogonal projection of v = proj, (v) = -5 onto the line L through -4 and the origin. 6…

A: Introduction:  The vector projection of a vector a on (or onto) a nonzero vector b, sometimes…

Q: Find a scalar equation of the plane containing the line and the point (-5, -1,5). x = 6 +8t, y=-1-3t…

A:

Q: Find a parametric representation of a straight line passing through (1,2,1) in the direction of…

A:

Q: Calculate the cross product assuming that u x w = (6, 3, 6) (-u+3w) x w =

A:

Q: 7. Find the scalar equation of any plane which contains the line = (1,2,1)+ t(3,6,-1)

A:

Q: Compute the distance between the vectors u = and

A: Given vectors are u=42−16 and v=4315. We have to find the distance between the vectors u→ and v→.…

Q: Let T: R2 R be a reflection in the line y = x. Find the image of each vector. (a) (0, 8) (b) (1,-1)…

A: Let T:R2→R2 be a reflection in the line y=x.

Q: Find the vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

A:

Q: Find the vector equation for the line of intersection of the planes 4x - y + 3z = 1 and 4x + 2z = −1…

A: Given:equation of two planes To find:vector equation of line that intersects these planes

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

A:

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: - 16] [1] Determine whether the vector v =| 17 |is spanned by the vectors and | 2 or not. 18

A: