Which one of the following is a point-normal form equation of the plane through the point (3, 1,2) with normal (1,4, 1)? A. (3,1,2). ((x, y, z)-(1,4,1))=9 OB. (3, 1, 2) ((x, y, z)-(1.4, 1)) = 0 OC. (1.4, 1) ((x, y, z)-(3,1,2)) = 9 CD.x+4y+z=9 OE (1,4, 1) (x,z)-(3,1,2)) = 0

Q: 2. Find T, N the unit bi-normal vector B, and k at the given t value. (2b) r(t) = ( cost, sint, In…

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Q: Find the normal vector to the plane that contains the point (1, 1, 3) and the line r(t)=(0,1,…

A: Let P be the point 1,1,3.Q be the point 0,1,2 on the line.Then, PQ→ = 0-1,1-1,2-3=-1,0,-1And the…

Q: Calculate the equation of the line that passes through the point (0, 1, 2) that is parallel to the…

A: We need to find the equation of the line passing through a point, parallel to a plane and…

Q: Find the equation of the plane that contains the line x = 1+t, y = 2+2t, z = 3- (1, -2,4). e point p…

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Q: Find equations of the following. 2(x - 4)2 + (y - 1)2 + (2 – 6)2 = 10, (5, 3, 8) (a) the tangent…

A: Given that: 2(x-4)2+(y-1)2+(z-6)2=10        and (5, 3, 8)

Q: Q2) Find T N „B of the vectors the curve r(t) = at the point (1, ,1)

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Q: Q2) Find the T „N of the vectors curve r(t) = at the point (1, 1)

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Q: 8. Find a normal for the plane that passes through the points: P(2,-2, 3), Q (3, 2, 1), R(-1,-4, 2)

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Q: Find a parameterization for a line passing through the points (1,1) and (5, 13) O x = t, y = 3t-2 O…

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Q: x-2 z+4 • Let L:*²=+3 = 2²+ and M: 2x - 3y +z = 6 are line and 3 2 5 plane and let P be the…

A: We have to find the equation of line

Q: The vertices of AJKL are J(-3, 4), K(3, 0), and L(-5, -4). The equation of the median JLis y = 0.…

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Q: Let line l : x=y/2=z/3 and point P(1,0,1). Find an equation of the plane (in point-normal form)…

A: Solution of given question is written in below steps.

Q: x = 1+2t Determine the distance between the lines L₁ y=-1-t, tЄR • z = 3t and L2: T = (1, 2, 3 1, 2,…

A: Step 1: Step 2: Step 3: Step 4:

Q: solve this question... please

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Q: Which of the following is a normal vector to the plane which is parallel to vectors (0,−3,1) and…

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Q: The plane given by x + y + 2z = 0 and the line given by x = 2 + t y = 1 - 2t z = 3 + t

A: The plane given by x + y + 2z = 0 and the line given by x = 2 + t;  y = 1 - 2t ;  z = 3 + t To find…

Q: Find equation of plane normal to line = = and pass through line x = y = z.

A: The equation of a plane passing through the point: x0, y0, z0 is defined as ax-x0+by-y0+cz-z0=0,…