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Elias Qadim Maraj
Asked: 2022-11-04T05:39:11+05:30 In:

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 parallel
B. are othogonal
C. satisfy `vecu .vecv =1`
D. satisfy `|vecu xx vecv| =hati +hatj +hatk`

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 parallel
B. are othogonal
C. satisfy `vecu .vecv =1`
D. satisfy `|vecu xx vecv| =hati +hatj +hatk`
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  1. 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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