1.

If the coordinates of the points A, B, C, D be `(1, 2, 3)`, `(4, 5, 7)`, `( 4, 3, 6)`and `(2, 9, 2)`respectively, then find the angle between the lines AB and CD.

Answer» Here, `vec(AB) = vecB - vecA = 3hati+3hatj+3hatk`
`vec(CD) = vecD-vecC = 6hati+6hatj+8hatk`
If we see the ratio of the coefficients of `hati, hatj and hatk` for both equations,
`=>3/6 = 3/6 = 4/8 = 1/2`
So, these two vectors are parallel.
So, the angle between `AB` and `CD` will be `0^@` or `180^@`.


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