मराठी

Find the vector equation of a line passing through a point with position vector 2i^-j^+k^ and parallel to the line joining the points -i^+4j^+k^ and -i^+2j^+2k^.

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प्रश्न

Find the vector equation of a line passing through a point with position vector `2hati - hatj + hatk` and parallel to the line joining the points `-hati + 4hatj + hatk` and `-hati + 2hatj + 2hatk`.

बेरीज
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उत्तर

Let A, B and C be the points with position vectors `2hati - hatj + hatk`, `-hati + 4hatj + hatk` and `hati + 2hatj + 2hatk`, respectively.

We have to find the equation of a line passing through the point A and parallel to vector BC.

Now, `vec(BC)` = Position vector of C – Position vector of `vecB`

= `(hati + 2hatj + 2hatk) - (-hati + 4hatj + hatk)`

= `2hati - 2hatj + hatk`

We know that, the equation of a line passing through a position vector `veca` and parallel to vector `vecb` is `vecr = veca + λvecb`

∴ `vecr = (2hati - hatj + hatk) + λ(2hati - 2hatj + hatk)` is the required equation of line in vector from.

[Here, `vec(BC) = vecb`]

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2021-2022 (March) Term 2 - Delhi Set 2

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