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)
A Aadil

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

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