If the direction ratios of a line are 1 + λ , 2 - λ , 4 and if it makes an angle of 6 0 o with the y -axis, then the sum of the values of λ is

Question

If the direction ratios of a line are 1 + λ , 2 - λ , 4 and if it makes an angle of 6 0 o with the y -axis, then the sum of the values of λ is,

MARKS App · Accepted Answer

The direction ratios of the line are 1 + λ , 2 - λ , 4 > direction ratios of the y -axis are 0,1 , 0 > So, cos ⁡ 60 o = 2 - λ 1 + λ 2 + 2 - λ 2 + 16 = 1 2 ⇒ 4 - 2 λ = 2 λ 2 - 2 λ + 21 ⇒ 4 λ 2 + 16 - 16 λ = 2 λ 2 - 2 λ + 2 1 ⇒ 2 λ 2 - 14 λ - 5 = 0 Hence, the sum of values of λ = 7

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