EXERCISE-4

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Embibe Experts Mathematics Solutions for EXERCISE-4

Simple step-by-step solutions to EXERCISE-4 questions of Vector Algebra from Beta Question Bank for Engineering: Mathematics. Also get 3D topic explainers, cheat sheets, and unlimited doubts solving on EMBIBE.

Questions from EXERCISE-4 with Hints & Solutions

HARD
JEE Main/Advance
IMPORTANT

Let ABCD be a tetrahedron such that the edges AB,AC and AD are mutually perpendicular. Let the area of triangles ABC,ACD and ADB be denoted by x,y and z sq. units respectively. Find the area of the triangle BCD.

MEDIUM
JEE Main/Advance
IMPORTANT

Find out whether the following pairs of lines are parallel, non-parallel & intersecting, or non-parallel & non-intersecting:

(b) r1=i^-j^+3k^+λi^-j^+k^r2=2i^+4j^+6k^+μ2i^+j^+3k^

MEDIUM
JEE Main/Advance
IMPORTANT

Find out whether the following pairs of lines are parallel, non-parallel & intersecting, or non-parallel & non-intersecting.

(c) r1=i^+k^+λi^+3j^+4k^r2=2i^+3j^+μ4i^-j^+k^

HARD
JEE Main/Advance
IMPORTANT

Given four points P1, P2, P3 and P4 on the coordinate plane with origin O which satisfy the condition OPn-1+OPn+1=32 OPn, n=2,3.
(b) If P1, P2, P3 lie on the circle x2+y2=1, then prove that P4 lies on this circle.

HARD
JEE Main/Advance
IMPORTANT

Solve the simultaneous vector equations for the vectors x and y.  x+c×y=a and y+c×x=b where c is a non zero vector.

HARD
JEE Main/Advance
IMPORTANT

Let a1-a2a1-b2a1-c2b1-a2b1-b2b1-c2c1-a2c1-b2c1-c2=0 and if the vectors α=i^+aj^+a2k^; β=i^+bj^+b2k^γ=i^+cj^+c2k^ are non-coplanar, show that the vectors α1=i^+a1j^+a12k^β1=i^+b1j^+b12k^ and γ1=i^+c1j^+c12k^ are coplanar.

HARD
JEE Main/Advance
IMPORTANT

If x×y=a, y×z=b, x·b=γ, x·y=1 and y·z=1, then find x,y & z in terms of a, b & γ.

HARD
JEE Main/Advance
IMPORTANT

Find the value of λ such that a,b,c are all non-zero and -4i^+5j^a+3i^-3j^+k^b+i^+j^+3k^c=λai^+bj^+ck^