(b) Given the line L: r = -2j – 7k + t(i +j- k) and the plane T: 2x + 3y – z = 7 (i) Find the point of intersection A between the line L and the plane n. (ii) Calculate the angle between L and n. (iii) Find the area of triangle OAB if B(-2,-4,µ)lies on the line L.

Q: Determine the angle between the two lines: 1₁: 7 = (1,0) + t(0, —2), t ¤ R x+2 y-3 and 1₂: *+² = −³.…

A: Given

Q: Find the point of intersection of the line 1,:r=-2i-7k+1(i+j-k) and the plane t: (b) 9n+7y+222=-83.…

A: The plane ? contains the point P−1,2,−4 and the below line l1. l1:r=2i−5j−3k+t−4i+2j+k

Q: Find the​ distance, d, between the point S(6,9,10) and the plane 10x+7y+1z=60.

A: Answer is 73/5√6.

Q: Give an equation of the plane determined by the intersecting lines L1 and L2 L1 : x = 2t y = 4 – t z…

A: The equation of two lines is given as follows: L1: x=2t, y=4-t, z=3+t L2: x=2+s, y=-3+2s, z=s The…

Q: Si -x- 2y - 3x + y R - x - 2y = 0, - x - 2y = 9, Find -dA, where R is the parallelogram enclosed by…

A:

Q: Find the shortest distance between the line L1:2x + y - 3 = 0 and the plane P1:3x - 4y + 12z + 5 =…

A: The formula for the distance between a point and a plane must be used to determine the shortest…

Q: 1. Find the angle between the lines L,:x = 3 + 8t, y = -6t,z = –7+ 24t and L2:x = 3 + 8t, y = 15t, z…

A: Solving only ques 1 according to guidelines.

Q: What angle does the line of interaction of the planes 2x+y-z = 0 and x+y+2z= 0 make with the…

A: The direction vector of the line of the interaction of the two planes is equal to the cross product…

Q: Find the point of intersection of the lines 2t + 1, y = -t+ 2, z = t+ 1 and x 2s + 2, y = s+3,z =…

A: Given lines are x=2t+1, y=-t+2, z=t+1x=2s+2, y=s+3, z=5s+6

Q: x-1 y+3 12-z Consider the following lines defined by I,: and l2: 9. =- %D 7 x = 2t + 10, y = 5t, z…

A:

Q: Let V1, V2, V3 be the vectors in R³ defined by V₁ = (c) Type the dimension of span{V₁, V2, V3}: -101…

A: Here,       v1 = (-10, 12, 12)t        v2 = (-37, 36, 17)t      v3 = (-7, 0, -19)t    (a) We see,…

Q: 3) Find the distances: a. Between ₁ = (3 + t, −2+ 3t, -t) and 1₂ = (1 + 2t, t, 5+ 4t). b. Between…

A: "Since you have posted multiple questions, we will provide the solution only to the first question…

Q: 1. Determine the point of intersection between the line, L: x = 3+t, y=4-5t, z=1-7t, te R, and the…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: 2. Find the vertex, focus, and directrix of the parabola. Then sketch the graph. (x − 3)² = 8(y + 1)

A: Solution:

Q: Find the point in which the line through the (3,-1,2) perpendicular to the plane x +2y -5 z = 4…

A:

Q: Find equations for the line perpendicular to the plane x + 5y - 2z = 6 and through the point of…

A:

Q: Find the angle between the following pair of lines: £ =2? =5] +k + 2(3 + 23 + 6k) and = 7i — 6k +…

A: A vector in the three dimensional space is represented by v=ai∧+bj∧+ck∧, where a, b and c are the…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.