Class 12 : Chapter 10 : Vector Algebra

 Q1 : Solve the following (3 marks each) (Solve any five)

1.  Vectors find the area of triangle RST, whose vertices are R(2, 2, 3), S(2, -2, 4) and T(4, 5, -1).
2. Use vector method to show that P,Q,R are Collinear – P(3, -5, 1), Q(-1, 0, 8) and R(7, -10, -6)
3. Find the angles between the lines whose direction ratios are 3, 2, -6 and 1, 2, 2. Find the angles of a triangle ABC whose vertices are A(-1, 3, 2), B(2, 3, 5) and C(3, 5, -2).
4. Prove that the points A(-2, 4, 7), B(3, -6, -8) and C(1,-2,-2) are collinear.
5. Find the angle between the lines whose direction ratios are: 2, -3, 4 and 1, 2, 1.
6. Using vectors, find the value of k such that the points (k, – 10, 3), (1, –1, 3) and (3, 5, 3) are collinear.

 Q2: Find the unit vector in the direction of the sum of the vectors (2)

a = 3i-j-3k

b = 2i-j-2k

Q 3: Find the vector joining the points A(2, -3, 0) and Q(– 1, – 2, 1) directed from A to B.(3)