Let L, be the line given by the intersection of two planes 2.r-y+z = 1 and x – y = -2 and let L2 be the line given by parametric equation x = 2 – t L2:{y = 3 – 5t z = t If u denotes the direction vector of L1 and u, denotes the direction vector of L2. Then (a) Find the vectors u and u. (b) Find the dot product of the vectors u and u. (c) Find the cross product of the vectors u and uz.

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: Determine a vector equation for the line that is perpendicular to 7 = (4, 1) + s(−3, 2), sER, and…

A: We need to find the equation of line perpendicular to r→=(4, 1)+s(-3, 2),  s∈ℝ and passing through…

Q: 32. Determine the vector equation of the plane that contains the following two lines. L1: = [4,-3,…

A: .

Q: Let L be the line through the point Q = (- 6, - 9, - 10) and direction vector d = [- 1, - 2, - 2]^T.…

A:

Q: The line (x-22-3, y = 2z) intersects the plane (x+3y-2+4= 0) at the point P, Find: a) the…

A:

Q: Find the vector equation of the line through the points P0(x0, y0, z0) and P1(x1, y1, z1).

A: P0x0, y0, z0 & P1x1, y1, z1. Now let a→ & b→ be the position vectors of the points P0x0, y0,…

Q: Find a direction vector for the line containing the origin (0, 0, 0) and the point (2, 3, – 1).

A: The given points are 0,0,0  and  2,3,-1

Q: 2. Find the equation of the planes: a) (in general form) that goes through the three points A(4, 0,…

A:

Q: III. Consider the line ₁ given by the symmetric equations +1=-y-1 B 2 and the line ₂ given by the…

A:

Q: Let L. be the line passing through the point P-(4, -3, 1) with direction vector a-[-4, 1, 1], and…

A:

Q: Find an equation of the plane containing the point (2,1,-1) and parallel to the plane 3x – y + 2z =…

A:

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 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: . The line (x-2z 3, y 22) intersects the plane (x+3y-:+4=0) at the point P, Find: (a) the…

A:

Q: Give an equation of the plane determined by the intersecting lines L1 and L2 = 2t 15 –t and L2 : {…

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:

Q: P(2,5, 4) and Q(8,3,3) Let be the line through P in vector direction (1,2,3) and let II be the plane…

A: