The points 2 -k- -k- 2 -2 -k- 2 -5 k- areA- collinearB- coplanar but not collinearC- noncoplanarD- none

The correct option is B coplanar but not collinearA⃗B= î +2k̂, A⃗C=ĵ+2k̂, A⃗D= 2î+ĵ+6k̂, A, B, C, D are not collinear. Box = 1 amp; 0 amp; 2 0 amp; ...

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Byju's Answer

Standard XII

Mathematics

Test for Coplanarity

The points 2 ...

Question

The points $2^i -^j -^k,^i +^j +^k, 2^i + 2^j +^k, 2^j + 5^k$ are

collinear

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coplanar but not collinear

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noncoplanar

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none

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Solution

The correct option is B coplanar but not collinear
$\to A B = -^i + 2^k, \to A C =^j + 2^k, \to A D = - 2^i +^j + 6^k,$
A, B, C, D are not collinear.
$B o x = ∣ ∣ ∣ ∣ \begin{matrix} - 1 & 0 & 2 0 & 1 & 2 - 2 & 1 & 6 \end{matrix} ∣ ∣ ∣ ∣ = - 1 (6 - 2) + 2 (0 + 2) = - 4 + 4 = 0.$
$∴$ A, B, C, D are coplannar.

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Similar questions

Q. The points

2^i -^j -^k,^i +^j +^k, 2^i + 2^j +^k, 2^j + 5^k

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(2^i + 3^j + 4^k) \times (^i -^j +^k)

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and

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Q. If

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, then the position vector of

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The points 2^i−^j−^k,^i+^j+^k,2^i+2^j+^k,2^j+5^k are

The correct option is B coplanar but not collinear→AB=−^i+2^k,→AC=^j+2^k,→AD=−2^i+^j+6^k, A, B, C, D are not collinear. Box=∣∣ ∣∣−102012−216∣∣ ∣∣=−1(6−2)+2(0+2)=−4+4=0. ∴ A, B, C, D are coplannar.

The points $2^i -^j -^k,^i +^j +^k, 2^i + 2^j +^k, 2^j + 5^k$ are