Let L, be the line passing through the points Q-(1, -4, 5) and Q-(-1,-7, 2) and let L2 be the line passing through the point P-(-23,0,-21) with direction vector -6, 3, -61" Determine whether L, and L2 intersect If so, find the point of intersection Q

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 the shortest distance from point P = (1,2,-3) to the plane which passes through (2,3,-1) and…

A:

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: What position vector is equal to the vector from (4.-3. - 2) to (-5, -8,7)? The position vector is…

A:

Q: ɔ determine if the points (1, 3, 3), (3, -1, 5), (5, 2, 0), and (3, 3, 4) ie in tne same plane.

A:

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: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(3, 4, 5) P2(2, 3,…

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: A vector orthogonal to the plane through the points (-1,0,0), (0, -2, -2), (2, 3, 4) is < 2, – 10, 6…

A:

Q: Find the unit vector represented by the directed line segment with initial point A (-2,1,1) and…

A: The vectorAB = B-A=(2,-3,4) -  (-2,1,1) = (4,-4,3) So the unit vector is :…

Q: In point P(-6,-8,8), express that vector that extends from P to Q(8, 6, -1) in: a. rectangular…

A:

Q: The line through the point (0, 1, 1) that is orthogonal to both ⟨0, -1, 3⟩ and ⟨2, -1, 2⟩.

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: The line that passes through the points (4, –2,0) and (1, 1, 1) is parallel to which vector? Check…

A:

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 projection of vector (0, 1, 0) into the line spanned by (0, 1,0) 0(-1,0, 2) 0(-1,3, 2) O (0, 3,…

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: 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 the symmetric equations of the line that passes through the point (3,6, –10) and is parallel to…

A: The line passes through a point means that the point lies on the line. The direction vector of a…

Q: Find the vector from the origin to the point of intersection of the medians of the triangle whose…

A: To determine the point of intersection of the medians of the triangle.

Q: Find projection of vector (0,1,0) into the line spanned by (0,1,0)

A: We have to find the projection of the vector (0,1,0) into the line spanned by (0,1,0).

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: 1- Find the direction of the vector with initial point P(-3,4,1) and terminal point Q(-5,2,2).

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

Q: What is the component form of the vector with an initial point of (-2,5) and a terminal point of…

A: Given that ,  The vector with  Initial Point = (-2 , 5) Terminal Point = (7 , -3).

Q: 1. Line L passes through point P(-2,5, 7) and having [4,-3, 2] as set of direction numbers. Find the…

A:

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

A:

Q: A line I through the point (5,3, -6) has direction cosines and Find the vector and parametric…

A: In this question, the concept of the vector equation of a line is applied. The vector equation of a…

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: What is the component form of the vector whose tail is the point (-2, 6), and whose head is the…

A: Answer is in step 2.

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: Write down the equation of the line that passes through the points (3,-2, 4) and (2, 3, -1). Using…

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 vector equation of a line passing through the point (-1, -2, 4) and perpendicular to both a =…

A:

Q: Consider the vector whose initial point is P(-6, 1) and terminal point is Q(-5, -3). Find the…

A: Recall: Position vector v→=a, b where a=x2-x1 , b=y2-y1 We have (x1, y1)=(-6, 1) and (x2, y2)=(-5,…

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: A vector orthogonal to the plane through the points (-1,0,0), (0, 0, -2), (2, 3, 4) is

A: We will solve the problem

Q: A direction vector passes through a unit cube from the (1/4, 1, 1/4) to the (1, 0, 3/4) positions.…

A: The direction passes through a unit cube from the 14,1,14 to the 1,0,34 positions. We have to find…

Q: Let l be the line through the point with coordinates (2,-1,0) in the direction of the vector…

A: Let L be the line through the point with coordinates 2, -1, 0 in the direction of the vector -11-1.…

Q: What position vector is equal to the vector from (- 2,9,3) to (-5, - 6,8)? The position vector is…

A: We have to find

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: The equation of the line with point (3, -6,8) and parallel to the vector (-1,2,3).

A:

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

A:

Q: Express (-1,2,4) as linear combination of x = (-1,2,0), y = (0,-1,1) and z = (3,-4,2) in the vector…

A: A vector is a quantity that has both magnitude and direction. It can be also defined as the…

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