Find the co-ordinates of a point on the line - p -2- i - j -3- k - 3- i -2- j -2- k at a distance of 5 units from the point 1- 3- 3

[ x+2 / 3 = 7+1 / 2 = 7 3 / 2 #160;; ...

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Standard XII

Mathematics

Cosine

Find the co-o...

Question

Find the co-ordinates of a point on the line $\to p = (- 2 \land i - \land j + 3 \land k) + λ (3 \land i + 2 \land j + 2 \land k)$ at a distance of 5 units from the point (1, 3, 3)

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Solution

$\begin{matrix} \frac{x + 2}{3} = \frac{7 + 1}{2} = \frac{7 - 3}{2} L e t B = (3 r - 2, 2 r - 1, 2 r + 3) C = (1, 3, 3) B C = 5 \sqrt{{(3 r - 3)}^{2} {(2 r - 4)}^{2} + {(2 r)}^{2}} = 5 \sqrt{9 (r^{2} + 1 - 2 r) + 4 {(r - 2)}^{2} + 4 r^{2}} = 5 \sqrt{9 (r^{2} - 2 r + 1) + 4 (r^{2} - 4 r + 4) + 4 r^{2}} = 5 \sqrt{17 r^{2} - 34 r + 25} = 5 17 r^{2} - 34 r + 25 = 25 17 r (r - 2) = 0 r = 0, 2 B \equiv (- 2, - 1, 3) (4, 3, 7) F o r r = 0 r = 2 \end{matrix}$

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Find the co-ordinates of a point on the line →p=(−2∧i−∧j+3∧k)+λ(3∧i+2∧j+2∧k) at a distance of 5 units from the point (1, 3, 3)

x+23=7+12=7−32LetB=(3r−2,2r−1,2r+3)C=(1,3,3)BC=5√(3r−3)2(2r−4)2+(2r)2=5√9(r2+1−2r)+4(r−2)2+4r2=5√9(r2−2r+1)+4(r2−4r+4)+4r2=5√17r2−34r+25=517r2−34r+25=2517r(r−2)=0r=0,2B≡(−2,−1,3)(4,3,7)Forr=0r=2

Find the co-ordinates of a point on the line $\to p = (- 2 \land i - \land j + 3 \land k) + λ (3 \land i + 2 \land j + 2 \land k)$ at a distance of 5 units from the point (1, 3, 3)