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Question
Position vector of the mid-point of line segment AB is `3hati + 2hatj - 3hatk`. If position vector of the point A is `2hati + 3hatj - 4hatk`, then position vector of the point B is ______.
Options
`(5hati)/2 + (5hatj)/2 - (7hatk)/2`
`4hati + hatj - 2hatk`
`5hati + 5hatj - 7hatk`
`hati/2 - hatj/2 + hatk/2`
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Solution
Position vector of the mid-point of line segment AB is `3hati + 2hatj - 3hatk`. If position vector of the point A is `2hati + 3hatj - 4hatk`, then position vector of the point B is `underlinebb(4hati + hatj - 2hatk)`.
Explanation:
Let, the position vector of point B is `xhati + yhatj + zhatk`.
Now given mid-point of line segment AB is `3hati + 2hatj - 3hatk` and position vector of point A is `2hati + 3hatj - 4hatk`.
∴ `((x + 2)/2)hati + ((y + 3)/2)hatj + ((z - 4)/2)hatk = 3hati + 2hatj - 3hatk`
∴ `(x + 2)/2` = 3, `(y + 3)/2` = 2, `(z - 4)/2` = – 3
`\implies` x = 4, y = 1, z = – 2
∴ Position vector of point B is `4hati + hatj - 2hatk`.
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