a. Show that |X — х У1 - у Z1 X2 - x Z2 - z = 0 Y2 - y |Xз — х Уз — у 23 — is an equation for the plane through the three noncollinear points P,(x1, y1, Z1), P2(x2, Y2, Z2), and P3(x3, y3, Z3).

Q: Let L₁ be the line passing through the points Q1=(-4, 2, -4) and Q2-(-1, 0, -6) and let L2 be the…

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Q: Let →a=a→= and →b=b→=. Find kk so that →aa→ and →bb→ will be orthogonal (form a 90 degree angle).…

A: We Know that, Two vectors u and v are said to be orthogonal vectors if and only if u . v=0 Here, a =…

Q: 3. For each set of e- i) determine the lines intersect point of inter ii) determine the lines do not…

A: a)i) To find the value of k so that the lines intersect, we need to solve for r and s in the system…

Q: Let P(x1, y1) and Q(x2, y2) be two points in the plane. Prove that the equation of the line through…

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Q: 7. a) Find the equation of the plane passes through the point P(1,2,-1), perpendicular to…

A: We have to solve given problems:

Q: 18. Find the points of intersection of the lines 4₁: R= 2i + 3j + 3k + t(i-2j + 5k) y +1 2 12: x + 3…

A: These two line not intersect

Q: J K L 1. Given: The coordinates of isosceles trapezoid JKLM are J(-b, c), K(b, c), L(a, 0), and…

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Q: Show that the line [x, y, z]= [5,-1,3]+[4,-5,2] lies on the planes 3x+2y-z = 10 and 7x+4y-4z=19.

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Q: Let R be the parallelogram enclosed by the lines x + 3y = 0, x + 3y = 2, x + y = 1 and x + y = 4.…

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Q: 3. Find the point in which the line x=+3t , y=1- 2t , and z=1+3t meets the plane x+y-z=1.

A: Here, given equation of line is,   And the given equation of plane is, From (1) and (2),

Q: Sherry is drawing a map of her workplace and her usual lunch meeting place on a standard (æ, y)…

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Q: 30 0= +시 +씨 2 |and 3x-y-z=3 -8/

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Q: A line, in R³ which passes through the point (xo, yo, zo) and with the direction vector (a, b, c),…

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Q: 7. Show that the equation of the plane that has x-intercept a, y-intercept b, and z-intercept c…

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Q: Find the equ. nf line through the Pont (-2,3,4) and Parallel to Planes: 2X+3y +42=5 3X + 4Y+52=6…

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Q: by the equations { L₁ : X Y Let L₁ and L2 be lines in a 3-dimensional space given { = = Z = 3 + 2t…

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Q: Evaluate v (x? v + x y z²) · dr where C is the line segment from (1, – 1,0) to (2,1,3) | Select one:…

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Q: Let V₁ = -4 1 | -12 B-B- V2 = 4 -3 11 -5 " and y = For what value of h is y in the plane spanned by…

A: and We have to find the value of .

Q: Use the equations to find дz Әх az ду - дz Әх əz Әх = and ƏF Әх ƏF əz and дz ду əz ду x2 - y2 + z² -…

A: x2-y2+z2-6z=7∂z∂x=-∂F∂x∂F∂z∂z∂y=-∂F∂y∂F∂z

Q: M3. Which of the following expresses the fact that the vectors u and v have the same length? (a) ū -…

A: M3. The two vectors u and v have the same length if: (a)u→·v→=v→·u→

Q: 16. For any vectors a, b and c, show that a. (axb) xc lies in the plane of a and b b. (a x b) X c =…

A: Step 1: Reference: Vector Calculus, Vector triple product

Q: 4. Given: AB with coordinates of A(-3,-1) and B(2, 1) A'B' with coordinates of A'(-1, 2) and B'(4,…

A: given,

Q: v1 =[ 2 5 1 ] , v2 =[ − 3 1 − 1 ] , b =[ 11 19 5 ] Show that b is in Span{v1,v2}. Express b as a…

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Q: 3-х у+4 16) Convert the symmetric equation of the line l: to the cartesian equation. 4 -7 IT-21

A: topic - cartesian equation of a line