MEDIUM
JEE Main/Advance
IMPORTANT
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If two pairs of opposite edges of a tetrahedron are perpendicular then-

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Important Questions on Vector Algebra

HARD
JEE Main/Advance
IMPORTANT
A non-zero vector a is parallel to the line of intersection of the plane determined by the vectors i^, i^+j^ and the plane determined by the vectors i^-j^, i^+k^. The possible angle between a and i^2j^+2k^ is-
HARD
JEE Main/Advance
IMPORTANT
Let a=2i^j^+k^, b=i^+2j^k^ and c=i ^+j^-2k^ be three vectors. A vector in the plane of b and c whose projection on a is of magnitude 23 is
MEDIUM
JEE Main/Advance
IMPORTANT
Let a, b, c are three non-coplanar vectors such that r1=ab+cr2=b+c-ar3=c+a+br=2a3b+4c. If r=ƛ1r1+ƛ2r2+ƛ3r3, then
HARD
JEE Main/Advance
IMPORTANT
A point M is taken on side AC of a triangle ABC, such that AM=13AC. A point N is taken on the side CB such that BN=CB then, for the point of intersection X of AB & MN which of the following holds good?
EASY
JEE Main/Advance
IMPORTANT
Vector A has components A1, A2, A3 along the three axes. If the co-ordinates system is rotated by 90° about z-axis, then the new components along the axis are
HARD
JEE Main/Advance
IMPORTANT
Let p, q, r be three mutually perpendicular vectors of the same magnitude. If a vector x satisfies the equation p×xq×p+q×xr×q+r×xp×r=0. Then x is given by
HARD
JEE Main/Advance
IMPORTANT
A vector which makes equal angles with the vectors 13i^-2j^+2k^,15-4i^-3k^ and j^, is
MEDIUM
JEE Main/Advance
IMPORTANT
The triple product d+aa×b×c×d simplifies to