CBSE Guess > Papers > Important Questions > Class XII > 2007 > Maths > Mathematics (Vector) By Mr. Manoranjan Behera

(Vector)

Q. 1. If is a unit vector and that find.

Q. 2. Express the vector =5 i-2j+5k as sum of two vectors such that one is parallel to the vector = and other is perpendicular to .

Q. 3. If a unit vector makes angle with , with  and an acute angle  with , then find the components of and the angle

Q. 4. If is any vector in space, then show that = + .

Q. 5. If are unit vector such that then find the value of

Q. 6. Prove that, for any two vectors .

Q. 7. Prove that if the vectors satisfy then

Q. 8. Prove that the points A, B and C with Position vectors respectively, and are collinear if and only if

Q. 9. If a, b, c are the position vectors of the non – collinear points A, B, C, respectively in space, show that is perpendicular’ to plane ABC.

Q. 10. Show that

Q. 11. Find and if

Q. 12. Given that and what can you conclude about the vectors ?

Q. 13. Prove that [] = 2

Q. 14. If any three vectors a, b and c are coplanar, prove that the vectors a + b, b + c and c + a are coplanar.

Q. 15. If a = 2i + 2j - k , b= 3i - j - k and c = i +2j - 3k, verify that a x (b x c ) = (a . c) b - ( a.b) c