HARD
JEE Advanced
IMPORTANT
Earn 100

Prove that the internal bisectors of the angles of a triangle are concurrent.

Important Questions on Vector Algebra

HARD
JEE Advanced
IMPORTANT
VECTOR AND 3-D GEOMETRY for JEE Main and Advanced>Chapter 1 - Vector Algebra>EXERCISE>Q 71
Prove that in any triangle, the line joining the mid-points of any two sides is parallel to the third side and half of its length.
MEDIUM
JEE Advanced
IMPORTANT
VECTOR AND 3-D GEOMETRY for JEE Main and Advanced>Chapter 1 - Vector Algebra>EXERCISE>Q 72
Prove that the straight line joining the mid-points of two non-parallel sides of a trapezium is parallel to the parallel sides and is half of their sum.
MEDIUM
JEE Advanced
IMPORTANT
VECTOR AND 3-D GEOMETRY for JEE Main and Advanced>Chapter 1 - Vector Algebra>EXERCISE>Q 73
Prove that the straight line joining the mid-points of the diagonals of a trapezium is parallel to the parallel sides and half of their difference.
HARD
JEE Advanced
IMPORTANT
VECTOR AND 3-D GEOMETRY for JEE Main and Advanced>Chapter 1 - Vector Algebra>EXERCISE>Q 74
If M, N are the mid-points of sides AB, CD of a parallelogram ABCD, prove that DM and BN cut the diagonal AC at its point of trisection which are also the points of trisection of DM and BN, respectively.
MEDIUM
JEE Advanced
IMPORTANT
VECTOR AND 3-D GEOMETRY for JEE Main and Advanced>Chapter 1 - Vector Algebra>EXERCISE>Q 75
Write down a unit vector in XY-plane, making an angle of 30° in anti-clockwise direction with the positive direction of x-axis.
MEDIUM
JEE Advanced
IMPORTANT
VECTOR AND 3-D GEOMETRY for JEE Main and Advanced>Chapter 1 - Vector Algebra>EXERCISE>Q 76
Find by vector method the horizontal force and the force inclined at an angle of 60° to the vertical whose resultant is a vertical force P.
MEDIUM
JEE Advanced
IMPORTANT
VECTOR AND 3-D GEOMETRY for JEE Main and Advanced>Chapter 1 - Vector Algebra>EXERCISE>Q 77
The velocity of a boat relative to water is represented by 3i^+4j^ and that of water relative to earth by i^-3j^. What is the velocity of the boat relative to the earth, if i^ and j^ represent velocities of 1 km/hr east and north, respectively?