the line passing through the points Q=(-4, -1, 4) and Q,=(-7, 5, 1). Find a value of k so the line L2 passing through the point P; = P;(-8, 15, k) with direction vector =[-3, -2, -4]T intersects with L7.

Q: Find a vector equation for the line through the point (-6, 4, 1) perpendicular to the vectors u =…

A: A line passes through the point -6,4,1 and perpendicular to the vectors u→=-1,-2,3 and v→=3,-8,-9 We…

Q: Find the distance from the point (3,-1, 4) to the line z -2+3t, y = -2t, z = 1+ 4t.

A:

Q: Let L7 be the line passing through the points Q=(-5, 4, 4) and Q2=(-6, 2, 2). Find a value so the…

A: We will solve the problem

Q: Find a vector equation for the line through the point (-3, –1,8) perpendicular to the vectors ū =…

A: vector equation can be find in the following way:-

Q: 2) L is the line passing through points (0, 0, 0) and (1, 1,1). M is the line passing through (2, 3,…

A: Direction vector of the first line is = (1,1,1)-(0,0,0)= (1,1,1) So the equation of the first line…

Q: Let L₁ be the line passing through the point P₁=(-8, 0, 11) with direction vector ₁-[-3, 2, 3]T, and…

A: Given The line L1 passing through the point P1=-8,0,11 with direction vector d1→=-3,2,3T The line L2…

Q: Write down the equation of the line that passes through the points (5, -1, 2) and (3, 1, 1). Using…

A:

Q: Let L, be the line passing through the points Q(-3, 2, -5) and Q2-(-6, 4,-4) and let L2 be the line…

A:

Q: Show that direction vectors of the lines 3 L: and

A: We have to find the direction vectors for the lines L1: x-32=y+14=z-2-1 and L2: x-35=y+1-2=z-32.

Q: The plane through the points (2, 1, - 1), (0, -2, 0), and (1, - 1, 2) is parallel | to the line x=…

A: Given that points are (2,1,-1), (0,-2,0) and (1,-1,2) The parametric equation is,…

Q: Let L, be the line passing through the points Q-(-1, -3, 1) and Q-(3, 3,-1). Find a value of k so…

A:

Q: 10

A:

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: Find a vector equation for the line through the point (-3, –1, 8) perpendicular to the vectors ū =…

A: Vector equation of the line passing through point (a,b,c) and perpendicular to vectors u→ and v→ is…

Q: Let L₁ be the line passing through the point P₁-(-3,-16, -2) with direction vector ₁-[2, 3, 1], and…

A: Given: L1 is a line passing through P1=-3, -16, -2 with direction d1→=2, 3, 1T and L2 is a line…

Q: Find a direction vector for the line through (4, 5, 3) and (2, – 3, – 1).

A: to find the direction vector

Q: Find an equation of the line through P(1,-2,4) with direction vector v=[2,4,-4] Find the equation of…

A: I am attaching image so that you understand each and every step.

Q: Find an equation of a plane through the point (1, -4, -3) which is orthogonal to the line x = -3 –…

A:

Q: Find the vector equation of a line that passes through the two points A(3,9,2) and B(−7,1, −4)

A: The given points are: A=3,9,2B=-7,1,-4  Therefore, A→=3i+9j+2kB→=-7i+j-4k  To find the vector…

Q: Let Lz be the line passing through the point P-(10, 1. –10) with direction vector d--2, -2, 3]", and…

A: We will use formula for the shortest distance.

Q: Let L7 be the line passing through the points Q1=(-5, -5,-3) and Q2=(-1,-3, 3) and let L2 be the…

A:

Q: The scalar equation of the line perpendicular to (x, y) = (5, 2) +r(1, -3) through the point (2, -2)…

A: The scalar equation of a line is of the form Ax+By+C=0

Q: 2. Find a vector equation of the line through (1, 0, −3) and (2, 4, 8). Make sure to justify your…

A:

Q: What is the vector equation of the line segment that connects point P(1,−1,2) to point Q (4,1,7)?

A: Given, A line segment passes through the points P1,-1,2 and Q4,1,7 We have, the vector equation of a…

Q: Then Duf(4, -3) in the direction of the vector 20 (-1, –2) is Let f(x, y):

A: Answer is mentioned below

Q: a) Find an equation of the line through P(1,-2,4) with direction vector v=[2,4,-4]

A: To find the equation of line.

Q: Let L7 be the line passing through the point P1=(-7,-15, 10) with direction vector d=[3, 3,-2]', and…

A: For skew lines ( lines in space which are neither parallel nor intersecting ) , the line of shortest…

Q: Find an equation of the plane through (1,8, 5) that is perpendicular to the line x – 2 = 3t, y + 3 =…

A:

Q: If P1 is (1,3,-1) and P2 is (-3,2,4), find the vector equation of the line P1P2. Determine the…

A:

Q: Find symmetric equations of the line passing through point P(2, 5, 4) that is perpendicular to the…

A:

Q: Let L, be the line passing through the point P1=(-1, -2, -2) with direction vector d-[-3, -3, 1]",…

A: L1 is the line passing through the point P1(-1 , -2, -2) with direction vectord→ = -3, -3, 1Tand L2…

Q: Find the distance of point 4(2-/3,2) from the line that passes through the origin and parallel to…

A: Distance of a point A(x1, y1) from the line ax+by+c=0 is given by d=ax1+by1+ca2+b2

Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(-1, 1, 5) P2(2, 5,…

A: Given Points - P1 = -1, 1, 5P2 = 2, 5, 0Vector P1 and P2 ,P1→ = -i+j+5k…

Q: Find general point for the lines The line through (0, -7, 0) perpendicular to the plane x + 2y + 2z…

A:

Q: Let Lz be the line passing through the points Q1=(-2, -4, 3) and Q2=(1, -2, 4) and let L2 be the…

A:

Q: Find a direction vector for the line containing the points (-1, 5, 2) and the point (2, 3, - 1).

A: We have to find a direction vector for the line containing the points -1, 5, 2 and 2, 3, -1. We know…

Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(1, 4, 5) P2(4, -2,…

A: Given that P1 1, 4, 5   and  P2 4, -2, 7. Compute the direction of vector P1P2 as follows.…

Q: The vector equation for the line passing through the points (-4, 1,0) and (4, 4,-3) is r(1)-

A: It is given that the line passes through the points (-4,1,0) and (4,4,-3). Consider that the vector…

Q: Write down the vector equation of the line that passes through the points (x,y,z) = (2,3,7) and…

A: The given problem is to find the vector equation of line that passes through the given two points.

Q: Find the equation of the line that passes through the point (3,4,5) and is parallel to the vector…

A: The equation of a line that passes through the point: x0, y0, z0 is L=x0, y0, z0+ta, b, c, where a,…

Q: The plane through the points (2, 1, - 1), (0, -2, 0), and (1, -1, 2) is parallel to the line x 1-t,…

A: equation of plane for non collinear points , x-x1y-y1z-z1x2-x1y2-y1z2-z1x3-x1y3-y1z3-z1 we will use…

Q: Let Lz be the line passing through the points Q=(-3, -3, 5) and Q2=(1,-9,–1) and let L2 be the line…

A: Given that the line L1 passes throogh the points Q1=-3,-3,5 and Q2=1,-9,-1The direction vector of…

Q: Let L7 be the line passing through the points Q-(-1, 2, 5) and Q2-(-4, 1, 3) and let L, be the line…

A: This question is related to three dimensional geometry.

Q: Let L7 be the line passing through the points Qz=(-1, -3, –3) and Q2=(3, -1, 1). Find a value of k…

A:

Q: Let L, be the line passing through the points Q-(1, -4, 5) and Q-(-1,-7, 2) and let L2 be the line…

A: To find: The intersection point of the lines L1 and L2. Given information: The line L1 passing…

Q: Find the coordinates of a point P on the line and a vector v parallel to the line x = 3 - 5t, y = -1…

A:

Q: Determine the vector equation for the line that is parallel to = [1,5,-7]+[2,-1,5] with the same…

A: The general equation of line in vector form is    .Then note the result : Line passing through the…

Q: Let Lz be the line passing through the points Qz=(2, 2, -4) and Q2=(8, –-1, 2) and let L2 be the…

A:

Q: Let L be the line passing through the point P1-(-2,-14, 4) with direction vector d=[-1, -3, 2]', and…

A: Solution: Let L1 be a line passing through the point P1=-2,-14,4 with direction vector d1→=-1,-3,2T.…

Q: Let L, be the line passing through the points Q, (5,-2, –3) and Q,-(-4, –11, 6). Find a value of k…

A: Equation of line in 3D