2) L is the line passing through points (0, 0, 0) and (1, 1,1). M is the line passing through (2, 3, 4)with direction vector (1, –1, 2). Where do lines L and M meet?

Q: The vector that has the same direction as ⟨3,4,3⟩ but has length of 4 is

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Q: 1 Suppose a line passes through the point (1, 1 and parallel to the 2' 3 plane x + y + z = 0. Then…

A: The direction vector of the normal to the plane is (1,1,1) Given that the line is parallel to the…

Q: Find terminal point Q of vector PQ =    <9, −2, 1>   with the initial point at…

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

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

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Q: 2- Suppose that vector v has initial point (-4,5) and terminal point (-1,12). a- Find the component…

A: a)A position vector v→ is defined as a line extending from the initial point (x1,y1) to the final…

Q: Consider the vector v between (-5,5, –3) and (1,1, 1).

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

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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…

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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…

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Q: as the sum of two orthogonal orthogonal to ư

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Q: The line that passes through the point (4, –2, 0) and parallel to the vector (1, 2, –3) has…

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Q: A plane contains the point  (1, -1,0 ) and its normal vector is \ vec {n} =  (6,24, -8 ). What is…

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

A: to find the direction vector

Q: Consider the vector v between (-5, 5, –3) and (1, 1, 1).

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Q: 2. Use a directed line segment to represent the vector. (а) и %3D (2, —4) (b) v = (2,4, –4)

A: Given that the vector a u=2,-4  b v=2,4,-4Solution a u=2,-4u=22+-42u=20  =25b v=2,4,-4v=22+42+-42v=6

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: The plane that contains the points (-2,1,0), (1, 0, –1) and (0, –1, 1) is orthogonal to which…

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Q: Find the component form and length of the vector v that has initial point (3, −7) and terminal point…

A: Given: Initial point (3,-7) and terminal point (-2,5).

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

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

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Q: a horizontal vector has initial point (-4,1) and has a magnitude of 7. What is the terminal point?…

A: The initial point of the vector is (-4, 1) and the magnitude of the vector is 7. Since it is a…

Q: Suppose L(5, 4) was reflected across the line y = x then translated along the vector . What is the…

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Q: 03, If a=(3,-1,1), for what value ofe is the vector b-(3,c,-1) perpendicular to a?

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Q: Suppose a line is given parametrically by the equation L (t) = (1- 3t,3t – 4, -3-t)- Then the vector…

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Q: Suppose (vector u)=(3,-4,-5) and Vector v=(2,-1,2)u+v=?u-v=?v-u=?3u=?(-1/4)v=?2u-3v=?I appreciate…

A: u=(3,-4,-5)v=(2,-1,2)

Q: The plane with normal vector (4, 6, 7) containing the point (-5,-1,5) has equation Ax + By + Cz = D.…

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Q: Show that ū = aitbj is perpendicular to the line ax+by=C by establishing that the slope of the…

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

A: Solution :

Q: Let L, be the line passing through the point P-(1, -7, 5) with direction vector d-[1,-2, 0], and let…

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Q: 5. Verify that its possible for a line with direction vector J=(2,1,-2) to lie flat on a plane with…

A: The vector equation of a plane is given by the expression . Here, and are the vectors that lie on…

Q: Suppose the vector ū =<3,1,-47 is translated so that it's heach is at the point C-1,2,3). where ito…

A: Given that the vector u→ = 3,1,-4 is translated such that its head is at the point (-1,2,3). We have…

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: Show that direction vectors of the lines 2 - 2 and L: are orthogonal.

A: The given lines are x-32=y+14=z-2-1  and x-35=y+1-2=z-32. The direction vectors of the given lines…

Q: Calculate the distance from point B=(−1,3,−1) to the plane that passes through point A=(3,2,−1) and…

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Q: Find the unit vector along the line joining point (2, 4, 4) to point ( - 3 , 2, 2). A) -0.8703ax -…

A: We can solve this as follows:

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

A: Let, Given vectors are P(-1,0,0), Q(0,0,-2) and R(2,3,4). We have to find non zero vector orthogonal…

Q: Use a directed line segment to represent the vector.u = (2, −4)

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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: Show that direction vectors of the lines L: and are arthogonal.

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Q: 5) Verify that it's possible for a line with direction vector d = (2,1,- 2) to lie flat on a plane…

A: For the vector representation of a plane , the vectors and lie on the plane. For the equation of…

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: 1. For the cross product between vectors a=[h, -1, 8] and b=[k, 5, 7] to be axb= [-47, -5, 17], what…

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Q: Use a directed line segment to represent the vector.u = (−3, −4)

A: The directed  line segment is the vector drawn from the any two points in the cartesian plane. The…

Q: Show that the lines with vector equations L1: 7 = (-2,1,0) + s(1, –1, 1), s ER L2 : 7 = (0,1,0) +…

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Q: 4. Show that u and v are orthogonal if and only if ||u + v||2 = ||u||2 + ||v||2. (Please avoid an…

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

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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

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.