1.

If a, b,c are the pth, qth, and rth terms of a HP, then the vectors ` vecu= a^(-1) hati +b^(-1) hatj +c^(-1) hatk and vecv = ( q -r) hati + ( q -r) hati + ( r-p) hatj + ( p-q) hatk`A. are parallelB. are othogonalC. satisfy `vecu .vecv =1`D. satisfy `|vecu xx vecv| =hati +hatj +hatk`

Answer» Correct Answer - B
Let A be the first term and D be the common difference of the corresponding AP. Then,
` 1/a = A + ( p -1) D, 1/b = A + ( q-1) D and , 1/c = A + ( r-1)D`
` a^(-1) (q-r) + b^(-1) (r-p) +c^(-1) (p-q) =0`
` Rightarrow vecu.vecv =0 Rightarrow vecu bot vecv`
Hence, ` vecu and vecv ` are othogonal vectors.


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