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Coordinate Geometry Quiz

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Question 1

Write the equation of a line parallel to the line  and passing through the point (1, -2, 3)

Question 2

Write the equation passing through the point (2, -1, 1) and parallel to the plane 3x + 2y – z = 7

Question 3

Let the coordinates of the points A, B, C be (1, 8, 4), (0, -11, 4) and (2, -3, 1) respectively. What are the coordinates of the point D which is the foot of the perpendicular from A on BC?

Question 4

The coordinates of the vertices P, Q and R of a triangle PQR are (1, -1, 1), (3, -2, 2) and (0, 2, 6) respectively. If RQP = θ, then what is PRQ equal to?

Question 5

Find the equation of the circle passes through the point (1, 3) and (2, -1), and has its centre on the line 2x + y – 4 = 0

Question 6

If (-1, 3) and (α, β) are the extremities of the diameter of the circle x2 + y2 – 6x + 5y – 7 = 0, find the coordinates (α, β).

Question 7

If  and  are vectors such that  and  then what is the acute between  and   ?

Question 8

A conical flask is full of water. The flask has base radius r and height h. the water is poured into a cylindrical flask of base radius mr. Find the height of water in the cylindrical flask?

Question 9

2.2cubic dm of grass is to be drawn into a cylinder wire 0.25cm in diameter. Find the length of wire?

Question 10

If  and  then what is the value of λ?
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