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
