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If position vectors of A, B, C, D are respectively $\vec{2i}+\vec{3j}+\vec{5k}, \vec{i}+\vec{2j}+\vec{3k}, -\vec{5i}+\vec{4j}-\vec{2k}$ and $\vec{i}+\vec{10j}+\vec{10k},$ then

Option 1)
$AB\parallel CD$

Option 2)
$DC\parallel AD$

Option 3)
$A, B, C,$ are collinear

Option 4)
$B,C,D$ are collinear

Answers (1)

best_answer

As we learnt

Position vector -

Let O be a fixed origin, then position vector of P is $\overrightarrow{OP}$

- wherein

$A= 2i+3j+5k$

$B= i+2j+3k$

$C=-5i+4j-2k$

$D=i+10j+10k$

$A\vec{B}= -i-j-2k= -\left ( i+j+k \right )$

$C\vec{D}= 6i+6j+12k$

$=6\left ( i+j+2k \right )$

So $\overrightarrow{AB}=\lambda \overrightarrow{CD}$

So $\overrightarrow{AB}\left | \right | \overrightarrow{CD}$

So

Option 1)

$AB\parallel CD$

Correct option

Option 2)

$DC\parallel AD$

Incorrect option

Option 3)

$A, B, C,$ are collinear

Incorrect option

Option 4)

$B,C,D$ are collinear

Incorrect option

Posted by

Aadil

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