JEE Main 2020 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 3 September 2020, Shift 2, Maths Q75

Question 75 of 75 in this shift, Maths question 25 of 25.

Let a plane P contain two lines

\vec{r} = \hat{i} + \lambda(\hat{i} + \hat{j})

\lambda \in \mathbf{R}

and

\vec{r} = -\hat{j} + \mu(\hat{j} - \hat{k})

\mu \in \mathbf{R}

. If

Q(\alpha, \beta, \gamma)

is the foot of the perpendicular drawn from the point M(1, 0, 1) to P, then

3(\alpha + \beta + \gamma)

equals __________.

Official answer

5.00

NTA final key (Sep 2020).

Chapter: Three Dimensional Geometry
Topic: Planes in 3D
Idea tested: Plane Containing Two Lines

Same idea in other shifts

Asked 4× in all

26 Jul 2022, Shift 2 · Q22The largest value of $a$ , for which the perpendicular distance of the plane containing the lines…HardNumerical value
26 Jun 2022, Shift 2 · Q15If the lines $\vec{r} = (\hat{i} - \hat{j} + \hat{k}) + \lambda(3\hat{j} - \hat{k})$ and…MediumSingle correct
2 Sep 2020, Shift 2 · Q67A plane passing through the point $(3,\,1,\,1)$ contains two lines whose direction ratios are $1,\,-2,\,2$ and $2,\,3,\,-1$ respectively.…MediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.