The points 2 ^ i − ^ j − ^ k , ^ i + ^ j + ^ k , 2 ^ i + 2 ^ j + ^ k , 2 ^ j + 5 ^ k are Options: A . &nbsp collinear B . &nbsp coplanar but not collinear C . &nbsp noncoplanar D . &nbsp none

Answer: Option B : B ⃗ A B = − ^ i + 2 ^ k , ⃗ A C = ^ j + 2 ^ k , ⃗ A D = − 2 ^ i + ^ j + 6 ^ k , A, B, C, D are not collinear. B o x = ∣ ∣ ∣ ∣ − 1 0 2 0 1 2 − 2 1 6 ∣ ∣ ∣ ∣ = − 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

Discussion Forum : Vector Algebra

Question -

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

Options:

A . collinear

B . coplanar but not collinear

C . noncoplanar

D . none

Answer: Option B
:
B

⃗ A B = -^i + 2^k, ⃗ A C =^j + 2^k, ⃗ 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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Discussion Forum : Vector Algebra

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