Test for Coplanarity
Trending Questions
Q. Let →a=^i+2^j+4^k, →b=^i+λ^j+4^k and →c=2^i+4^j+(λ2−1)^k be coplanar vectors. Then the non-zero vector →a×→c is :
- −10^i−5^j
- −14^i−5^j
- −10^i+5^j
- −14^i+5^j
Q. The points 2^i−^j−^k, ^i+^j+^k, 2^i+2^j+^k, 2^j+5^k are
- collinear
- coplanar but not collinear
- noncoplanar
- none
Q. Let ^a=^i+^j+^k, ^b=^i−^j+2^k and ^c=x^i+(x−2)^j−^k. If the vector ^c lies in the plane of ^a and ^b, then x equals
- \N
- 1
- -4
- -2
Q. If a, b, c are respectively the pth, qth, rth terms of an A.P., the ∣∣
∣∣ap1bq1cr1∣∣
∣∣ =
- 1
- -1
- 0
- pqr
Q. Let a, b, c be distinct non - negative numbers. If the vectors a^i+a^j+c^k, ^i+^k and c^i+c^j+b^k, are coplanar then c is
- AM of a and b
- GM of a and b
- HM of a and b
- None of the above
Q. Given: →a, →b and →c are coplanar.
Vectors →a−2→b+3c, −−→2a+→3b−→4c and−→b+→2c are non-coplanar vectors.
Vectors →a−2→b+3c, −−→2a+→3b−→4c and−→b+→2c are non-coplanar vectors.
- True
- False
Q. The vectors →a=x^i+(x+1)^j+(x+2)^k, →b=(x+3)^i+(x+4)^j+(x+5)^k and →c=(x+6)^i+(x+7)^j+(x+8)^k are coplanar for
- all values of x
- x < 0
- x > 0
- None of these
Q. The sum of the distinct real values of μ, for which the vectors, μ^i+^j+^k, ^i+μ^j+^k, ^i+^j+μ^k are co-planar, is:
- 0
- −1
- 1
- 2
Q. A vector (→d) is equally inclined to three vectors →a=^i−^j+^k, →b=2^i+^j and →c=3^j−2^k. Let →x, →y, →z be three vectors in the plane of →a, →b;→b, →c;→c, →a, respectively. Then which of the following is INCORRECT?
- →x.→d=0
- →y.→d=0
- →z.→d=0
- none of these
