MEDIUM
JEE Advanced
IMPORTANT
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Let ABC be a triangle, the position vectors whose vertices are 7j^+10k^,-i^+6j^+6k^ and -4i^+9j^+6k^. Then, ΔABC is 

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Important Questions on Vector Algebra

EASY
JEE Advanced
IMPORTANT
The sides of a parallelogram are 2i^+4j^5k^ and i^+2j^+3k^. The unit vector parallel to one of the diagonals is
HARD
JEE Advanced
IMPORTANT
If A4,0,3 and B14,2,5, then which one of the following points lies on the bisector of the angle between OA and OB ( O  is the origin of reference)?
EASY
JEE Advanced
IMPORTANT
If point i^+j^, i^j^ and pi^+qj^ +rk^ are collinear, then
EASY
JEE Advanced
IMPORTANT
If a,b and c are non-coplanar vectors and λ is a real number, then the vectors a+2b+3c,λb+μc and 2λ-1 c are coplanar when
EASY
JEE Advanced
IMPORTANT
A vector a has components a1,a2&a3 in a right-handed rectangular Cartesian system OXYZ. The coordinate system is rotated about Z-axis through the angle π2. Find the components of a in new system.
HARD
JEE Advanced
IMPORTANT
Find the magnitude and direction of r1-r2 when r1=r2=5 and r1 points North –East while points r2 North –West.
HARD
JEE Advanced
IMPORTANT
Let OACB be a parallelogram with O at the origin and OC as a diagonal. Let D be the midpoint of OA. Using vector methods, prove that BD and CO intersect in the same ratio, determine this ratio.
HARD
JEE Advanced
IMPORTANT
ABC is a triangle with the point P  on side BC such that 3BP=2PC, the point Q is on the line CA such that 4CQ=QA. Find the ratio in which the line joining the common point R of AP and BQ and the point S divides AB.