Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

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

 

 Since \underset{AB}{\rightarrow}=\left ( p.v \right )\vec{B}-\left ( p.v \right )\vec{A}

So that \underset{AB}{\rightarrow}=\left ( i+2j+3k \right )-\left ( 2i=3j+5k \right )

= -i-j-2k

Similarly \underset{CD}{\rightarrow}=6i+6j+12k

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

So that ratios are equal. so they are parellal

\underset{AB}{\rightarrow}\left | \right |\underset{CD}{\rightarrow}


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

divya.saini

View full answer

Similar Questions

Latest Question