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3D Geometry question

2021 · 25 Feb · Shift 2 · Q44
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3D Geometry question

2021 · 25 Feb · Shift 2 · Q44

JEE MainMathematics3D GeometryNumerical+4 / −1
A line 'l' passing through origin is perpendicular to the lines l1:r→=(3+t)i^+(−1+2t)j^+(4+2t)k^l2:r→=(3+2s)i^+(3+2s)j^+(2+s)k^{l_1}:\overrightarrow r = (3 + t)\widehat i + ( - 1 + 2t)\widehat j + (4 + 2t)\widehat k{l_2}:\overrightarrow r = (3 + 2s)\widehat i + (3 + 2s)\widehat j + (2 + s)\widehat kl1​:r=(3+t)i+(−1+2t)j​+(4+2t)kl2​:r=(3+2s)i+(3+2s)j​+(2+s)k If the co-ordinates of the point in the first octant on 'l2‘ at a distance of 17\sqrt {17}17​ from the point of intersection of 'l' and 'l1' are (a, b, c) then 18(a + b + c) is equal to ‾\underline{\hspace{2cm}}​.
Numerical answer
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