JEE Main 26 Feb 2021 Shift 1 Solved Paper

Given (λ,2,1) be point on the plane which passes through (4,−2,2) and plane is perpendicular to line joining P and Q. Given, AB is perpendicular to PQ i.e., AB⋅PQ=0
Now, AB‌‌=(4−λ)

∧

i

+(−2−2)

∧

j

+(2−

∧

k

‌‌=(4−λ)

∧

i

−4

∧

j

+

∧

k

PQ‌‌=(−1+2)

∧

i

+(−16+21)

∧

j

+(23−29)

∧

k

‌‌=

∧

i

+5

∧

j

−6

∧

k

‌‌=(4−λ)

∧

i

−4

∧

j

+

∧

k

PQ‌‌=(−1+2)

∧

i

+(−16+21)

∧

j

+(23−29)

∧

k

‌‌=

∧

i

+5

∧

j

−6

∧

k

Hence, AB⋅PQ=0
⇒‌(4−λ)(1)+(−4)(5)+(1)(−6)=0
⇒‌4−λ−20−6=0
⇒‌λ=−22
‌ Then, ‌(‌

λ

11

)2−(‌

4λ

11

)−4=(‌

−22

11

)2−(‌

4×(−22)

11

)−4
=‌‌4−(−8)−4=8