Find the vectors T, N, and B at the given point. r(t) =   (1, (1/3), 2) Find the normal and osculating planes at the given point.

Q: (a) Find the equation of the plane p containing the point P (4, 3, 4) and with normal vector (2,…

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Q: Find a vector equation of a plane having x-intercept 4, y-intercept -1, and a z-intercept of 5.…

A: The x-intercept is 4. The y-intercept is -1. The z-intercept is 5.

Q: X = Find the vector equation for the line of intersection of the planes x - 5y + 5z = −5 and x + 5z…

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Q: Given the points M[0.1, -0.2, -0. 1), N(-0.2, 0.1, 0.3), and P(0.4, 0, 0.1), find: (a) the vector…

A: This question can be solved using the concept of finding the vector joining two points and dot…

Q: Find the vector equation for the line passing through the points P₁(-3, 6, 8) and P₂(−6, 0, 12). 0 0…

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Q: X = Find the vector equation for the line of intersection of the planes x − 5y + 5z = −5 and x + 5z…

A: Given the equation of planes x-5y+5z=-5 and x+5z=1. To find the vector equation for the line of…

Q: Find a vector equation with parameter t for the line through the point (7,0, –7) and parallel to the…

A: We have to find a vector equation with parameter t.

Q: A vector equation for the line through the points A (3, -4, -3) and B (3,4,2) is (x, y, z) = . (You…

A: Concept to be used:If a line passes through two points A,Bwith position vectors aand brespectively,…

Q: The line (x-22-3, y = 2z) intersects the plane (x+3y-2+4= 0) at the point P, Find: a) the…

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Q: Find an equation for the plane that passes through the point (3, -2, 1) normal to the vector n = 2i…

A: Given:A point (3, -2, 1) normal to the vector n = 2i + j + kThe normal vector can be written as,

Q: Find a vector normal to the plane -2x - 3y = 12 - 4z.

A: Given  a vector -2x-y=12-4z. We need to find the vector normal to the plane.

Q: - 3)² = 81 then, find its ce or a=<3, -1

A: 1. Given: The points are 2,3,-6 and -1, 4, 5 To find the distance between the given points. The…

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: Find a vector equation for the line through the point P = (-3, 5, -4) and parallel to the vector v =…

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Q: Find the equation of the plane with normal vector n = (8, 7, 3) passing through the point (4,,9) in…

A: Use equation of plane and put value

Q: Determine the equation of the plane with a point 'a' and the normal vector 'n': a = (−1, 2, −3)t ,…

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Q: Q8. Find the equation of the plane passes through the point (1,2,3), parallel to the vector…

A: We have to find the equation of a plane passing through a given point and parallel to two vector.…