If (-2, 3), (4, -3) and (4, 5) are the mid-points of the sides of a triangle, find the coordinates of its centroid.

Q: Find the distance from the point P(1, 4, 0) to the plane through A(0, 0, 0), B(2, 0, -1), and C(2,…

A: Given points A0,0,0 , B2,0,-1 & C2,-1,0The direction ratios of AB⇒2-0,0-0,-1-0=2,0,-1Similarly…

Q: Let A(2, -3) and B(-2,1) be vertices of a triangle ABC. If the centroid of this triangle moves on…

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Q: Find the angle between the planes 2x + y- 3z 2 and -x + 2y - z= 1.

A: We can solve the given problem as follows:

Q: Find 3 different homogeneous coordinate representations for the Cartesian point (1,-2)

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Q: Determine the shortest distance from the point (3, 4, 5) to the line through the origin parallel to…

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Q: The distance from (-3,-4,-7) to the yz-plane is (A) -4 (B) 4 (C) -3 (D) 3 (E) 7

A: The distance(d) between two points (x1,y1,z1) and (x2,y2,z2) in a cartesian coordinate system is…

Q: Find a parametric representation of a straight line passing through (1,2,1) in the direction of…

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Q: A point moves so that sum of the squares of its distances from the vertices of a triangle is always…

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Q: Find the vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

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Q: Find the distance between (1,-2, - 1)and the plane through the points (1, 2, 3)and (3 , 2, 1)and…

A: Given information: The plane passes through the points (1, 2, 3) and (3 , 2, 1) and perpendicular to…

Q: Let A(2, -3) and B(-2,1) be vertices of a triangle ABC. If the centroid of this triangle moves on…

A: Vertices of triangle ABC are A(2,-3) , B(-2,1) and the centroid of this triangle moves on the line ,…