1.Find the distance between the point (3, 1, -2) and the plane x + 2y - 2z = 4.

Q: 1. Consider the vectors ū = (-1, 2), ở = (2,3) and w = (a, 3). (a) Find the resultant of ū and i,…

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Q: Find a unit vector perpen dicular to the plane of the vectors a = (2, -3,1) and b = (1, 2, -4)

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Q: Plane passing through point P0 (1, 2, 1) and perpendicular to vector (1, -1, 2) Find the equation…

A: Given:  Plane D1 : passing point P0(1, 2, 1)                 perpendicular vector (1, -1, 2) Plane…

Q: 11. Let / be the intersection of the two planes 2x - 3y + 4z = 2 and x-z = 1 a. Find a vector…

A: Let l be the intersection of the following two planes(a) To find a vector equation of l.(b) To find…

Q: b) Consider the vectors u = (2c, 2, −4), v=(c, c, 3)and w = (-1, 2, 3). Find the value(s) of…

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Q: Find the vector n= normal to the plane passing through the points (0, -3, 0), (2, -1, 0) and (-2,…

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Q: Find a vector ī that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4, –2),…

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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: What is the vector equation of the line segment that connects point P(1,−1,2) to point Q (4,1,7)?

A: Given, A line segment passes through the points P1,-1,2 and Q4,1,7 We have, the vector equation of a…

Q: Find a vector equation and a parametric equation for the line that passes through the point (5, 1,…

A: We have to solve given problem:

Q: 2. (6 marks) Find the vector equation of a plane a) Passing through the point A(-1, 2, -3) and…

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Q: Find parametric equations for the line through the point P(-5,6,7) and perpendicular to the vectors…

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Q: Find the equation of the plane P spanned by vectors  v = (2,1, 3)  and w = (1,2,-1)  containing the…

A: The given problem is to find the equation of plane P that is spanned by given two vectors and…

Q: (a) Determine the vector equation and the Cartesian equation of the plane B passin by the points…

A: This is a problem of vector calculus.

Q: Find the projection of v = [-3, 3, 6] onto the line L with vector equation x=td where d = [4, -3, 1]

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