b) Let l and l2 be lines in 3 space such that 2. 4 passes through the point with coordinates (3, 4, 5) in the direction of 1 2 passes through the points with coordinates (8, 0, 1) and (8, 0, -1) Write down the equations of l and 2 in parametric as well as Cartesian forms.

Q: 1. What is the vector and parametric forms of the equation of the line passing through points…

A: This question can be solved using the concept of vector and parametric equation of line passing…

Q: fficients of x, y, and z in the given equation of the plane. ..... z= -7+ 9t. pe expressions using t…

A: Find parametric equation.

Q: 4. Find parametric equations of a line passing through (1, 2, 3) that is parallel to the plane…

A:

Q: Find sets of (a) parametric equations and (b) symmetric equations of the line that passes through…

A:

Q: Give the parametric and symmetric equations of the line that passes through the point (4, -3,5) and…

A: Using the dot product equal to zero for perpendicular to the vectors.

Q: Find a parametric representation of the line through the points P(4,1,2) and Q(3,5,7)

A:

Q: Consider three points in three-dimensional space: A=(11,2,−5),B=(2,−5,11),C=(−5,11,2). Find the…

A: The equation of a line passing through the point (a, b, c) and in the direction <h, k, l> is…

Q: 33) Given point P(1,2, 3) and vector n= î + ĵ , find point Q on the x-axis such that PQ and în are…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find symmetric and parametric equations of the line through the two points (−3, 5, 2) and (1, −3,…

A:

Q: Find a set of parametric equations of the line through the point (1,-2, 3) and perpendicular to the…

A: Concept: As we know that a equation of the line through the point (α,β,γ) and perpendicular to the…

Q: 6. Write vector and parametric equations of the plane. a) parallel to the xz-plane and through the…

A:

Q: Consider the point (3,4,5) What is the projection of the point on the xy-plane?

A: The given point is (3,4,5).

Q: Determine vector and parametric equations for the line in R that passes through the points A(1,0, 1,…

A:

Q: A line passes through the point (6,9, - 8), and is parallel to the vector 9i + 8j + 5k. Find the…

A: Given: a line passes through the point(6,9,-8) and is parallel to the vector 9i+8j+5k To find :…

Q: Find the equation of the plane parallel to the line r = 2i + t(−4i + 3j + 8k) and containing the…

A:

Q: Give the parametric and symmetric equations of the line that passes through the point (2,6, –1) and…

A: To find equation of line passing through the point 2,6,−1 and perpendicular to both vectors −4,3,−5…

Q: 5. Find the parametric equations of the line that passes through the point (0, 1, 4)and is…

A: Given two vectors, u=2, -5, 1v=-3, 1, 4 Also, given the point, P=0,1,4 The cross product of u and v…

Q: 19) Find the equation for the line in 3-space passing through the points (2,5,3) and (3, -3, 7)…

A:

Q: Find the vector, parametric, and symmetric equa lines: (a) the line perpendicular to x+7_y-4 with 3…

A:

Q: 17. Explain why it is not possible for a line in three-space to be represented by a scalar equation…

A:

Q: 3. Give the parametric and symmetric equations of the line that passes through the point (4,-3,5)…

A:

Q: Find a set of parametric and symmetric equations of the line satisfying the following Passing…

A:

Q: (1 point) The planes 4x + 4y- z= 10 and 5x + 4y-4z 9 are not parallel, so they must intersect along…

A: The  intersection of two planes is always a line .

Q: Give the parametric equation of the line that passes through the point (−4, 3, −5) and is…

A:

Q: 4. (a) Find a parametric equation and symmetric equation of the line that pases through the point…

A: We have a point P(2,-1,3) and a vector  i^+2j^-3k^ We have to find a parametric equation and…

Q: 3. Give the parametric and symmetric equations of the line that passes through he point (4, –3, 5)…

A:

Q: Find a set of parametric and symmetric equations of the line satisfying the following Passing…

A: We have to find the equation of the line passing through the point (1,2,-1) and normal to the plane…

Q: Determine the vector and parametric equations of the line through A(6,2,5) and B(9,2,8)

A: Given points , A(6,2,5) B(9,2,8) Therefore a=6i+2j+5k b=9i+2j+8k

Q: Find a parametric equation and symmetric equation of the line that pases through the point (2, -1,3)…

A:

Q: Give the parametric and symmetric equations of the line that passes through the point (4, –3,5) and…

A: we have to find the equation of line which is passes through the given point and perpendicular to…

Q: Determine whether the solution space of the system Ax = 0 is a line through the origin, a plane…

A:

Q: Find a set of parametric equations and symmetric equations of the line ` con- taining the point P(1,…

A: Given Point is (1,-2,3) And Plan is : 2x-y+3z=6

Q: Find a set of parametric and symmetric equations of the line satisfying the following Passing…

A: According to the given information it is required to find a set of parametric equation of the line…

Q: Find parametric (or vector) and symmetric equations of the line which pass through the points P,…

A: P11, 4, 6 & P22, -1, 3. Vector equation of a line passing through two points with position…

Q: 1. Find the vector and parametric equations for a line passing through (7,-4, 2) and parallel to the…

A: We have to find the vector and parametric equation of the line

Q: Provide the parametric and symmetric equations of the line that passes through the point (4, -3, 5)…

A:

Q: 1. a. Show that two lines with direction vectors d, = (2,3) and d, = (6,-4) are perpendicular. %3!…

A:

Q: find a set of parametric equations of the line through (2,8,3) and (11,20,21)

A: The line through the points (2,8,3) and (11,20,21)

Q: Which of the following point is the projection of the point (0, 4, 2) on the yz-plane?

A: In this question we have to find the projection of the point on the yz-plane.

Q: 5. Find the parametric equations of the line through A (-1, 2, 3) and B (2, 2, -3). Hence find where…

A: The set of parametric equations of a line passing through the points (x1,y1,z1) and (x2,y2,z2) are…

Q: Sketch the curve in the Complex Plane i) Iz-31 = \Z+3il %3D

A: Just use the definition of modulus of a complex number and you are done.

Q: -) Find the distance from the point (4, 22, 6) down to the ry-plane. ) Find the distance from the…

A:

Q: 5- Determine the value for x such that the points A(-1,3,4),B(-2,3,-1), and c(-5,6,x) all line on a…

A:

Q: Give the parametric and symmetric equations of the line that passes through the point (4,-3, 5) and…

A:

Q: Give the parametric and symmetric equations of the line that passes through the point (5,−1,3) and…

A: