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  • Show that the vectors 2i − 3 j + 4k and − 4i + 6 j − 8k are collinear.

Q.11  Show that the vectors 2 \hat i -3 \hat j + 4 \hat k and - 4 \hat i + 6 \hat j - 8 \hat k  are collinear.

Answers (1)

best_answer

Let 

\vec a =2 \hat i -3 \hat j + 4 \hat k

\vec b=- 4 \hat i + 6 \hat j - 8 \hat k

It can be seen that

\vec b=- 4 \hat i + 6 \hat j - 8 \hat k=-2(2 \hat i -3 \hat j + 4 \hat k)=-2\vec a

Hence here \vec b=-2\vec a

As we know

Whenever we have \vec b=\lambda \vec a, the vector \vec a and \vec b will be colinear.

Here \lambda =-2

Hence  vectors 2 \hat i -3 \hat j + 4 \hat k and - 4 \hat i + 6 \hat j - 8 \hat k  are collinear.

Posted by

Pankaj Sanodiya

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