1. Let P(19, 19), Q(40, 57), and R(48, 32) be three points in the xy plane. (a) Determine the vectors a =QP, b = RP, and c = RQ (algebraically) and draw them on the ry plane below. Q (b) Calculate a +c and then write an equation relating a, b, and c. R P (c) Find the length of the vector c above. Don't evaluate the square root.

Q: bäi The cross product of the vectors 3ax + 4ay – 5az and -ax + ay - 2az * ,is -3ax+11ay-7az O -3ax +…

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Q: 17. 17. Choose the vector orthogonal to the plane through the following three points P.Q and R. 다음 세…

A: Given three points P(7,-2,0), Q(3,1,3) and R(4,-4,2)  We have to find vector orthogonal to the plane…

Q: A, B, and C are 3 distinct points with non-zero position vectors a, b, and e respectively. a If a x…

A: Given three distinct points are A, B, C. with position vectors a, b, c respectively.…

Q: A linear combination of of u = 3 and v= 4 will give a plane in R³. Given that the point (2, 1, −1)…

A: Consider the given linear combination, u=132 and v=-144 will give a plane in ℝ3. The equation of a…

Q: Let U = (2,1,0), V = (1,0,1), and W = (2, −1,1). Find the plane through U, V, and W, expressed in…

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Q: Find an equation of the plane that passes through the point P(4, 7, 1) and has the vector n = (1, 3,…

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Q: Consider the vectors a = (-1,–2, 3), b = (3,0, –2), v = (2, –5, –4) and the plane P given by 2x + y…

A: The given vector is; a→=-1,-2,3b→=3,0,-2v→=⟨2,-5,-4⟩and Plane P is;2x+y=z+13⇒2x+y-z=13…

Q: Read the foilowng queohon below and Choose the correct answew' What is a divecton vector for He…

A: We need to find the direction vector. NOTE - As per Bartleby's guidelines we can only solve one…

Q: Which of the following vectors is orthogonal to the plane 3(x - 7) + (y + 8) - 5z = 15? O O O

A: Given equations of plane 3(x-7) +(y+8)-5z=15this is an equation of the form a(x-x1)+b(y-y1)+…

Q: 4. Given that '(t) = (6t², 2t + 4) and that (2) = (2, 8), find r(t), where we are assuming that the…

A: We have to find the r(t)

Q: Consider the planes x – 10y – 2z = 3 and 2x – y + z = -13. Find the following. 1. A vector…

A: The given planes are: x-10y-2z=3 and 2x-y+z=-13 Let us assume z=t on the line of intersection, where…

Q: 4. Find the vector equations for the line of intersection of the following planes: 2x – y – 5z = -14…

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Q: The vector parallel to intersection line of the two planes 4x-y+z=2 and 2x+y-2z=3 is: O0 -3i+6j-3k…

A: Two planes are given: 4x-y+z=2 and 2x+y-2z=3

Q: 10) Eind the eçuation of the plane Contaihins the two vectors 2and ,and the point PU2ー)

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Q: Let r = 2ji+yj+z¡k, r2 = ¤2i+ yzj + 22k and r3 = Lzi+ Yaj+ z3k be the position vectors of points…

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Q: Show that the vectors 1 – t,1+ 2t² , t² +t+1, t² + 2tare linearly dependent and indicate how one of…

A: Given Vectors:V1 = 1-tV2 = 1+2t2V3 = t2+t+1V4 = t2+2tgiven vectors are linearly dependent, then…

Q: Given a point P- (0,,2) and the and i- L2,3,0>. eguation for the plane whose a vectors Find that con…

A: Given: The point P0,1,2 and the vectors u→=1,0,1  and v→=2,3,0, To find: The equation of the plane…

Q: If a line is parallel to the vector 4i + 10j + 7k and passes through the point P = (7,7,4), then the…

A: Solution

Q: Find an equation of the plane that passes through the point P(4, 6, 3) and has the vector n = (1,6,…

A: I have stated the used formula in the solution.

Q: 1. Consider the plane II1 : 3z + 2y + x = 2. (a) If II2 : 2z – 3y = 1 is another plane. Are the…

A: Here we solve the three dimensional geometry problem.

Q: Find a vector parallel to the line of intersection of the planes x+ 3y – 2= =13, and 3x – 4y + = =-8…

A: Solution is here

Q: Let P = (-2,0, 5), Q = (3, 1, 1), and R = (0,0, 4) and define a = PÓ and b= PR. Find (d) The…

A: Given three points are: P:-2,0,5, Q:3,1,1, R:0,0,4 The position vectors for the given points are:…

Q: Find a vector, in component form, that is orthogonal to the plane containing the points P=(2,0,-4),…

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Q: Find the equation of the plane E passing through the point P(2,3,1) and parallel to the vectors K =…

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Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = (4,…

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Q: Prove that the intersection line of the planes P₁: 2x -y - 2z = 0 and P₂:x-2y+z = 0 is parallel to…

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: If a line is parallel to the vector 3i + 9j+ 6k and passes through the point P = (5, 5, 4), then the…

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Q: 12. a. Use vectors to show that the distance from P;(x1, Y1, Z1) to the plane Ax + By + Cz = D is…

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Q: Find the vector form of the equation of the line inR3 that passes through P = ( - 1, 0, 3) and is…

A: Find the vector form of equation of line passing through point  P=-1,0,3 and perpendicular to the…

Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = ( 5 , −…

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Q: га- Find an equation that describes all values of a, b, and c for which the vector w = |b| is NOT a…

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Q: Let ri = xi+yıj+z¡k, r2 = x2i+ Y2j + z2k and r3 = x3i+ Y3j + z3k be the position vectors of points…

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Q: Consider the points K (−1, 0, 7) and M(1, −2, 5), the vector MN = (1, 4, −3), and the line  I with…

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Q: Find the equation of the plane through P(2, – 1,1) that is parallel to Il: 2x + 3y + z – 12 = 0. %3D

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Q: Use the component form to generate an equation for the plane through P1(4, 1, 5) normal to n1 = i -…

A: Concept - If a plane is passing through (x0, y0, z0) and normal vector is A, B, C.Then equation of…

Q: Find a nonzero vector parallel to the line of intersection of the two planes 5y – 4x + z =-1 and –…

A: The line of intersection of two planes is orthogonal to their respective normals.

Q: Consider the points K (−1, 0, 7) and M(1, −2, 5), the vector MN = (1, 4, −3), and the line  I with…

A: We have to solve given problems:

Q: 5) Consider the vector ū = (1,2, –2) and the points Q(5, 5, 2) and R(3,0,0). Answer the following…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 5) Consider the vector ū = (1,2, –2) and the points Q(6, 5, 2) and R(3,0, 0). Answer the following…

A: Plane and vector

Q: Find an equation of the plane that passes through the point P(3, 5, 1) and has the vector n = (1, 8,…

A: As we know that; The equation of the plane which is passing through a point Px0,y0,z0 and a normal…

Q: Find an equation of the plane that passes through the point P(5, 6, 2) and has the vector n = (1,7,…

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Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = (5, 2,…

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Q: 1. Show that the vectors u̟ and uz parallel to lines L1 and L2 respectively, are orthogonal. L1: x =…

A: The given equations of lines are: L1:x=5-2t, y=-7+t, z=6+4t and L2:x=2+3t, y=5+2t, z=1+t Rewriting…

Q: (3) Write the equation of the plane which is perpendicular to the vector ñ² = (2₁-1₁-2) and touches…

A: To find- Write the equation of the plane which is perpendicular to the vector n→ = 2, -1, -2 and…

Q: Find an equation of the plane that passes through the point P(4, 5, 3) and has the vector n = (1, 8,…

A:

Q: 6.) Consider the points P(-1,2,5), Q(2, –3, 0) and (i) Write an equation of the plane containing t

A: Equation of plane: We know that, the equation of plane that passes through point (x, y, z) is given…

Q: Find a vector parallel to the line of intersection of the planes 4х + 2y - 33 %3D17 and 3x - 4y…

A: Vector parallel to the Inter section of two planes  a and b is cross product of a and b Let m is a…

Q: 2. Determine the vector equation of the plane that contains the following two lines. L1: 7 = [ 4,…

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Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = ( –…

A: Topic = Vector

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.