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### 12th Maths - 30 Days – Scoring Worksheet - Day 10

XII Mathematics

30 Days –Scoring Worksheet - Day 10

Part 5  Marks

1.      Find the non-parametric form of vector equation, and Cartesian equations of the plane passing through the points (2, 2,1), (9, 3, 6) and perpendicular to the plane  2 x + 6 y + 6 z = 9

2.      Find parametric form of vector equation and Cartesian equations of the plane passing through the points (2, 2,1), (1,2, 3) and parallel to the straight line passing through the points (2,1,3) and (1, 5,8)

3.      Find the parametric vector, non-parametric vector and Cartesian form of the equations of the plane passing through the three non-collinear points (3, 6,2), (1,2, 6) , and  (6, 4, –2)

4.      Prove by vector method that if a line is drawn from the centre of a circle to the midpoint of a chord, then the line is perpendicular to the chord.

5.      Prove by vector method that the median to the base of an isosceles triangle is perpendicular to the base.

6.      Prove by vector method that an angle in a semi-circle is a right angle.

7.      Prove by vector method that the diagonals of a rhombus bisect each other at right angles.

8.      Using vector method, prove that if the diagonals of a parallelogram are equal, then it is a rectangle.

S. Saravana Kumar M.Sc., B.Ed., PGDCA.,

PG Asst., Jazz Public Mat Hr Sec School, Melur , Madurai Dist