TS EAMCET · Maths · Three Dimensional Geometry

Suppose $L_{1}$ and $L_{2}$ are two lines having the direction ratios $1, - 2, - 2$ and $0, 2, 1$ respectively. If the direction cosines of a line perpendicular to both $L_{1}$ and $L_{2}$ are $l, m, n$ then $|l| + | m | + | n ∣ =$

A $3$
B $\frac{5}{3}$
C $\sqrt{3}$
D $\frac{7}{3}$

Verified Solution

Answer & Solution

Correct Answer

(B) $\frac{5}{3}$

Step-by-step Solution

Detailed explanation

∙ Lines having direction cosines l,m,n & 1,-2,-2 are perpendicular ⇒l-2m-2n=0 .....i ∙ Lines having direction cosines l,m,n & 0,2,1 are perpendicular…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Suppose L1 and L2 are two lines having the direction ratios 1,-2,-2 and 0, 2, 1 respectively. If the direction cosines of a line perpendicular to both L1 and L2 are l, m, n then l+|m|+|n∣=

Step-by-step Solution

Suppose $L_{1}$ and $L_{2}$ are two lines having the direction ratios $1, - 2, - 2$ and $0, 2, 1$ respectively. If the direction cosines of a line perpendicular to both $L_{1}$ and $L_{2}$ are $l, m, n$ then $|l| + | m | + | n ∣ =$