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प्रश्न
Find the vector and the cartesian equation of the line that passes through (−1, 2, 7) and is perpendicular to the lines `overset->r = 2hati + hatj -3hatk + lambda(hati + 2hatj + 5hatk)` and `overset->r = 3hati + 3hatj - 7hatk + mu(3hati - 2hatj + 5hatk)`.
उत्तर
Line perpendicular to the lines `overset->r = 2hati + hatj -3hatk + lambda(hati + 2hatj + 5hatk)` and `overset->r = 3hati + 3hatj - 7hatk + mu(3hati - 2hatj + 5hatk)`.
Has a vector parallel; it is given by `overset->b = overset->b_1 xx overset->b_2 = |(hati, hatj, hatk),(1, 2, 5),(3, -2, 5)|`
= `20hati + 10hatj -8hatk`
∴ Equation of line in vector form is `overset->r = -hati + 2hatj + 7hatk + a(10hati + 5hatj - 4hatk)`
And equation of line in cartesian form is `(x + 1)/10 = (y - 2)/5 = (z - 7)/-4`
