Find k so that the points P(0, 1, 1), Q(-1, 1, 3), and R(-3, 1, k) are on the same line (collinear).

Q: Calculate F. dĩ, where C is the square of (1,1, 1), (–1, 1, 1), (–1, –1,1) and (1, –1,1), with…

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Q: Prove that the three points (;q, yx), (x2, y2), and (x3, y3) are collinear (lie on the same line) if…

A: Given : The three points are : x1, y1, x2, y2 and x3, y3 Now we have to prove that  x1, y1, x2, y2…

Q: Find symmetric equations for the line through (1, 3, -2) and perpendicular to both u and v, where u…

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you.  If…

Q: Calculate F . dr, where C is the square of (1,1, 1), (–1,1, 1), (-1,–1,1) and (1,–1,1), with…

A: Let F→x,y,z=zex-yezi→+2cosy-xezj→+ex-xyezk→ and C is the square with vertices…

Q: Let g(x) = b,x² + bx + b,x + bg, x E R be a polynomium whose graph intersects the points (-2, 4),…

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Q: Find the point on the plane x+5y+2z=14 closest to the point​ (1,1,1).

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Q: Show that three points P , Q, R are collinear (lie on a line)if and only if −→P Q × −→P R = 0.

A: Given: Show that three points P, Q, and R are collinear (lie on a line) if and only if PQ→×PR→=0

Q: Find a plane containing the point (7,-8,8) and the line F(t) = +t

A: Given that, the point is 7,-8,8 and the line is r→t=-6,-8,-7+t6,8,4. From the given line, the point…

Q: Find the directed distance from the given line to the given point. (-1, 6) (5, 4) (10, 8) (1, 2)…

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Q: Find the intersection of the plane: x - z = 6, and the line r(t) = (1,0, -,1) + t(4,9,2)

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Q: 4. Prove that the midpoint of the line segment connect- ing the points (x 1, X 2, - . . , Xp) and…

A: The midpoint of a segment can be considered to be the average…

Q: For 3 and 4given the translation rule: T(x,y) (x+2,y-3)

A: Find the image of (5,-1) and preimage of (-6,7)

Q: Find the condition for the points (a, 0). (h, k){0,b) when ab = 0 to be collinear.

A: Find the condition for the given points to be collinear.

Q: Find an equation of the plane passing through the three points given.P = (2, −1, 4), Q = (1, 1, 1),…

A: To find the equation of the plane passing through the three pointsP =x1,y1,z1= (2, −1, 4), Q…

Q: Find a plane through P (2, 1, 1) and perpendicular to the line of intersec- tion of the planes:…

A: find a plane through P2,1,1 and perpendicular to the line of intersection of the planes  2x+y-z=3 ,…

Q: Parametrize the directed line segment which joins the point −2 + 3i to the point 5 − 7i, that is,…

A: The parametric equation on a line passing through the points x1,y1 and x2,y2 is given as follows:…

Q: Find an equation of the plane passing through the three points given.P = (5, 1, 1), Q = (1, 1, 2), R…

A: GivenP=(5,1,1) , Q=(1,1,2) and R=(2,1,1)To find equation of plane passing through the three points.

Q: Find an equation for the plane through P(1,4, 4) that contains the line of intersection of the…

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Q: Find the distance between the planes 5x - 3y + z = 9 and 5x - 3y + z = -6.

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Q: find an equation of the plane passing through the three points given.  P = (2, 0, 0), Q = (0, 4, 0),…

A: Equation for plane P is written in vector form as: n.(x,y,z)=d In scalar form equation is written as…

Q: Evaluate (6x-3y)dA where Ris the parallelogram with vertices (2,0), (5,3), (6,7) and (3,4)using the…

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Q: The plane that passes through  (9, 0, −3)  and contains the line  x = 6 − 3t, y = 2 + 5t, z = 4 +…

A: Given : A point (9,0,-3) where the plane passes through.             A system of equations for line…

Q: Find the work done by the Öeld F = yzi + (xz + 3)j + xyk along the line joining the point A(1, 2, 0)…

A: Given field is,  F = yz i^ + xz+3 j^ + xy k^   The given points is A(1, 2, 0) and B(2, 0, 3). So,…

Q: Let L be the line that passes through the point  (1,3,1 ) and orthogonal to the plane 3x-2y + 5z =…

A: In the question we have to find interacting points at which line and plane intersect.

Q: 4. If possible, express t as a linear combination of u, v, and w. t = (2, 13, 5), = (1,2, 1), v = (-…

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Q: Which of the following points are collinear to (1,0) and (3,6)? Show graphically and analytically.…

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Q: Find an equation of the plane through the three points given: P = (0, 1, 0), Q = (-3, 4, – 1), R =…

A: Recall: Equation of the Plane containing three points P,Q and  R is expressed as ,            r→ .n∧…

Q: prove Theorem 4P.1 Theorem 4P.1 There are exactly six lines in the four-point geometry.

A: The known fact is that in four point geometry, any two distinct points have exactly one line on both…

Q: Find an equation of the plane passing through P = (1, 2, 3), Q = (0, 0, 3), and R = (−2, 5, 4).

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Q: FIR R whose by (1,213) qnd (4,5,6) a) Find Iinear mapping Image is generated

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Find t for the following terminal points: (a) P(0, 1), t = (0) P(-, ), t =| (c) P(-1,0), t = (d)…

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Q: the set A = {2+x², 3+ 5x – 4x²} C P2(R) - -) Show that A is linearly independent.

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Q: Find the symmetric equations of the L that is parallel to the two planes x + 2y - z= 2 and x + 6y+ z…

A: Given: Two planes, P1: x+2y-z=2, P2: x+6y+z=-3, Point P1, 2, 3

Q: Find the linear equation of the plane through the point (0, 1, 1), (1, 0, 1), and (1, 1, O)

A: Consider the point (0,1,1). Take option (a) x-y-z+2=0-1-1+2=0 Take option (b) -x+y-z+2=-0+1-1+2=2≠0…

Q: Find the coordinates of the reflection without using the coordinate plane. P (4,6) over the x-axis.

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Q: Find the condition for the points(a, 0).(h, k)(0, b) when ab 0 to be collinear.

A: When points are colllinear area should be 0Therefore, 12a01hk10b1=012ak1b1+1hkb1=0

Q: Prove that if the points (x1, y1) and (x2, y2) lie on the same line as (x∗1 , y∗1 ) and (x∗2 , y∗2…

A: Prove that if the points (x1, y1) and (x2, y2) lie on the same line as (x∗1 , y∗1 ) and (x∗2 , y∗2…

Q: Find an equation of the plane through the points P(0, 1, 1), Q(1, 0, 1), and R(1, 1, 0).

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Q: Find the coordinates of the intersection point of the lines x_1 + 3x_2 = 3 and −2x_1 + 4x_2 = 1 in…

A: Solved below

Q: Use Lagrange Multiplier to find the Point P (x,y,z) closest to the origin on the plane containing…

A: The equation of the plane passing through the three points can be obtained using the matrices. The…

Q: Suppose v,, v,,V3 are distinct points on one line in R" . The line need not pass through 29 the…

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Q: Find // (4x + 5y)dA where R is the R parallelogram with vertices (0,0), (-3,1), (2,4), and (-1,5).…

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Q: The distance from the point K(3, -2, 0) to the xz- plane is Select one: O-2 O √13 O 0 02 None of…

A: We need to find out the distance between the given point and xz plane.

Q: Find a line equation through the point P(1,2,3) and parallel to the line of intersection of the…

A: Planes as:                       2x+y-z=3x+2y+z=2;   The given point as:                        (1,…

Q: Find an equation of the plane through the three points given: P = (0,0, 2), Q = (-4, 1, –1), R = (2,…

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Q: -:Q1 Evaluate , (x- 2y) dA, where R is the parallelogram in the xy-plane with vertices (0,0), (4,1),…

A: The objective is to evaluate ∫∫Rx-2ydA where R is the parallelogram in the xy plane with vertices…

Q: Prove that three points (x1, yl), (x2, y2) and (x3, y3) are collinear ( on the same straight line)…

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Q: Find points in the Euclidean plane corresponding to the points e₁-[3,-5,-1], e2=[1,-2,2], e3 [2,1,0]…

A: By Pn , we denote the projective space of dimension n, defined as follows: Pn=Rn+1 \ {0}~, where '~'…

Q: Find the set of points that is satisfied the condition described by |z – 2i|+ |z + 4i| = 10

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