Let the lines L_1: \overrightarrow{r}=\lambda(\stackrel{\^}{i}+2 \stackrel{\^}{j}+3 \widehat{k}), \lambda \in R L_2: \overrightarrow{r}=(\stackrel{\^}{i}+3 \stackrel{\^}{j}+\widehat{k})+\mu(\stackrel{\^}{i}+\stackrel{\^}{j}+5 \widehat{k}) ; \mu \in R intersect at the point S. If a plane a x+b y-z+d=0 passes through S and is parallel to both the lines L_1 and L_2, then the value of a+b+d is equal to [25-Jun-2022-Shift-1]

JEE Main 25 June 2022 Shift 1 Solved Paper

Section: Mathematics

Question : 28 of 90

Marks: +1, -0

Let the lines
L1:

→

=λ(

+3‌widehat‌k),λ∈R
L2:

→

+widehat‌k)+µ(

+5‌widehat‌k);µ∈R
intersect at the point S. If a plane ax+by−z+d=0 passes through S and is parallel to both the lines L1 and L2, then the value of a+b+d is equal to

[25-Jun-2022-Shift-1]

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