Let L_1: { { }}↖{→}=({ {\i}↖{\^}}-{ {\j}↖{\^}}+2 { {\k}↖{\^}})+λ({ {\i}↖{\^}}-{ {\j}↖{\^}}+2 { {\k}↖{\^}}), λ ∈ {\R} {\L}_2: { { }}↖{→}=({ {\j}↖{\^}}-{ {\k}↖{\^}})+µ(3 { {\i}↖{\^}}+{ {\j}↖{\^}}+ {\p} { {\k}↖{\^}}), µ ∈ {\R} and {\L}_3: { { }}↖{→}=δ(ℓ { {\i}↖{\^}}+ {\m} \hat{{j}}+ {
} { {\k}↖{\^}}) δ ∈ {\R}Be three lines such that L_1 is perpendicular to L_2 and L_3 is perpendicular to both L_1 and L_2. Then the point which lies on {\L}_3 is [30-Jan-2024 Shift 2]

Question

Let L_1: { {}}↖{→}=({ {\i}↖{\^}}-{ {\j}↖{\^}}+2 { {\k}↖{\^}})+λ({ {\i}↖{\^}}-{ {\j}↖{\^}}+2 { {\k}↖{\^}}), λ ∈  {\R}  {\L}_2: { {}}↖{→}=({ {\j}↖{\^}}-{ {\k}↖{\^}})+µ(3 { {\i}↖{\^}}+{ {\j}↖{\^}}+ {\p} { {\k}↖{\^}}), µ ∈  {\R} and  {\L}_3: { {}}↖{→}=δ(ℓ { {\i}↖{\^}}+ {\m} \hat{{j}}+ {
} { {\k}↖{\^}}) δ ∈  {\R}Be three lines such that L_1 is perpendicular to L_2 and L_3 is perpendicular to both L_1 and L_2. Then the point which lies on  {\L}_3 is  [30-Jan-2024 Shift 2]

Examsnet · Accepted Answer

Correct Answer is :  (−1,7,4)

JEE Main 30-Jan-2024 Shift 2 Solved Paper