Find a vector equation and parametric equations for tha line sagmant that joins P to o. A-6, 8, 0). Q(, -1, 7) vector aquation parametric quations x(), v), 2t)

Q: Find both the vector equation and the parametric equations of the line through (0,0,4) in the…

A: Explanation of the answer is as follows

Q: 4. (a) Find the unit vector that has the same direction as (3,4,0). (a) Calculate the distance…

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

Q: Let ū = (0, 1, –1), ū = (1, 1, 0) and w = (2, 1, 1). a) Show that ū, ī and w lie in the same plane…

A: Vectors u ,v and w lie in same plane if u.(vxw) = 0 Here u = (0,1,-1) v = (1,1,0) w= (2,1,1) 3…

Q: 1. Determine the vector and parametric equations of the line passing through P(-2, 3, 5) and Q(−2,…

A: According to our guidelines we can only solve the first question and rest of the questions can be…

Q: Let ū = (0, 1, –1), v = (2, 1,0) and w = (4, 1, 1). a) Show that ū, ū and w lie in the same plane…

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Q: 1.Find the vector equation and parametric equations of the line passing through the point P(5, 6, 7)…

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Q: Find the vector and parametric equations for the line through the point P(-5, -3, -4) and the point…

A: Given: P(-5,-3,-4) and Q(-2,2,-5) To find the vector r(t) and the parametric equations for x(t),…

Q: Find the vector and parametric equations for the line through the point P = (-1, 4, −4) and the…

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Q: 1. Determine vector and parametric equations of the plane that contains the points A(1, 2, -1), B(2,…

A: Since you have posted multiple questions. we will solve first question only due to the bartleby…

Q: Let L be the line with parametric equations x = −3+2t y = 8+t z = 5+3t Find the vector equation for…

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Q: Consider the points A(2,-1, 3), B(7,0, 5) and C(0, 1, 7), and the line with symmetric equations x=2_…

A: Question 3 and 4 has been solved as per the requirement of the student.     This question can be…

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: Give a vector parametric equation for the line through the point (3,4,−2) that is parallel to the…

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Q: Given a point M = (5,–3,–2) on a line in space and a parallel vector to the line defined as vector d…

A: Parametric equations of a line  in 3-D space are given byx = x0 + t a , y = y0 + t b , z = z0 + t c…

Q: 1. Letz =1+i,1,=-1+i, locate the numbers z+ z, and , vectorially in the rectangular coordinate…

A: We are Given that : z1=1+iz2=-1+i ⇒z1+z2=(1+i)+(-1+i)=2i and  ⇒z1-z2=(1+i)-(-1+i)=1+i+1-i=2

Q: 5. Find all vectors such that x v = . 6. Find parametric equations for the line through (2,4,-2)…

A: (6) Given :- The parametric equations for the line through 2,4,-2 that is perpendicular to plane x…

Q: Find the equation for the plane through the point Po = (7,2,3) and normal to the vector n= 4i + 6j +…

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Q: (a) Find a vector parallel to the line of intersection of the planes -x + 3y + 4z : 0 and -x - 3y –…

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Q: 1. Find equation of plane P containing point P,: (1,2,3) and the vectors v = (2,1,2) and w = (3,…

A: Solution:-Here we have to find the equation of the plane containing points P0:(1,2,3) and vectors…

Q: The Cartesian equation of the straight line tangent to the plane curve given parametrically by the…

A: This question can be solved using the concept of tangent and normal under application of…

Q: (a) Determine the vector and parametric equations of the line containing points E (-1, 5) and F (6,…

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Q: Find the vector and parametric equations for the line through the point P(3, 1, 5) and the point…

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Q: 1. Write vector and parametric equations of the line. a) parallel to the line x+6y = 1 and through…

A: Parametric and vector equation of line

Q: 3) Write down the equation of line in a vector parametric form, scalar parametric form and standard…

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Q: Find both the vector equation and the parametric equations of the line through (0,0,0) and (5,2,4),…

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Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

A: Here we find the vector and parametric equations of line.

Q: Find the vector and parametric equations for the line through the point P = (-4, –4, 5) and the…

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Q: Find both the vector equation and the parametric equations of the line through (3,3,1) that is…

A: If line perpendicular to both lines the direction vector perpendicular to both parallel vectors of…

Q: 3) Find a vector equation and parametric equations for the line segment that joins (-2, 4, 0) to…

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Q: A point P(3,0,5) lies on a plane that can be defined by the scalar equation Ax+By+Cz+ D = 0. A…

A: the scalar equation of a plane with normal  vector n=(A,B,C) is  AX+BY+CZ+D=0

Q: 7. Find the vector and parametric equations of the plane that is parallel to the yz-plane and…

A: W e have to find the equation of plane.

Q: Find both the vector equation and the parametric equations of the line through (0,0,4) in the…

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Q: A line passes through the point (8, - 5,7), and is parallel to the vector 9i + 7j + 10k. Find the…

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Q: Suppose a plane containts the point P = (1, 2, 3) and vectors å = (4, 1, 0) and b = (6, 0, 1). Use…

A: Solution

Q: Find parametric equations for the line through p (2,3,0) and perpen-dicular to the vectors u =(1,…

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Q: If the vector equation of a line is 7=(3, -5)+t(-2, 3), t€ R. the parametric equations are Ox=3-2t,…

A: Topic:- application of geometry

Q: Find the vector and parametric equations for the line through the point P= (3,0, –1) and the point Q…

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Q: If the vector v has initial point P, what is its terminal point? v = (-7, 0, 7), P(8, 0, –8) (x, y,…

A: in 3d space, if point P(X1, Y1, Z1) is the initial point and point T(X2, Y2, Z2) is the terminal…

Q: 1. Let L be the line through (2, 5) and parallel to v = (3, -1). (a) Parametric equations of L are y…

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

Q: Let ü = (0, 1,-1), e - (2, 2,0) and i - (4, 2, 2). a) Show that ü, and w lie in the same plane when…

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Q: Find the vector and parametric equations for the line through the point P(-1, 3, 4) and the point…

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Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

A: u = < 0,2,2>  w = < 2,-2,0>  U× W is perpendicular to both u and w

Q: Find the equation for the plane through the point Po = (2,7,6) and normal to the vector n= 3i + 5j +…

A: Given:-normal, n=3i+5j+6kpoint on the plane, P0=2, 7, 6let (x, y , z) on the plane vector (x-2)i+…

Q: A line has parametric equations x = 2 +3t, y = 1 + 2t, z = -6 - t, fort that belongsto the family of…

A: given parametric equation of line  is x=2+3ty=1+2tz=-6-t

Q: Find the distance of the point (2, 6, –4) from the line r(t) = (-1 + 31, –1+41, 5 – 2t). Give a…

A: Consider the given point as, 2,6,-4  And the line -1+3t,-1+4t,5-2t

Q: Find vector and parametric equations of the plane that contains the point P = (-3,1,0) and is…

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Q: =(2,3,1) Determine the vector equation and the Cartesian equation of line 1₁ passing by points A =…

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Q: The Cartesian equation of the straight line tangent to the plane curve given parametrically by the…

A: Explanation of the answer is as follows

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.