✓ Board-verified
Mathematics · 2022 · 2 marks
CBSE 2022 · Region 2 · Set 1 · Q6
Write the cartesian equation of the line PQ passing through points P (2,2,1) and Q (5,1,-2). Hence, find the y-coordinate of the point on the line PQ…
Write the cartesian equation of the line PQ passing through points $\displaystyle \mathrm{P}(2,2,1)$ and $\displaystyle \mathrm{Q}(5,1,-2)$. Hence, find the y-coordinate of the point on the line PQ whose z -coordinate is -$\displaystyle 2$ .
Marking-scheme solution
Required equation of line is given by\[\frac{x-2}{3} = \frac{y-2}{-1} = \frac{z-1}{-3}\]putting $\displaystyle z = -2$, we get $\displaystyle \dfrac{y-2}{-1} = \dfrac{-3}{-3} = 1$\[y - 2 = -1 \Rightarrow y = 1\]
All Three Dimensional Geometry questions2022 question paperNCERT solutions: Three Dimensional GeometryPractice Three Dimensional Geometry →
More from Three Dimensional Geometry
- Find the image A^′ of the point A(1,6,3) in the line x/1=(y-1)/2=(z-2)/3. Also, find the equation of the line joining A and A^′. OR Find a point P on…2025
- Find the values of λ, for which the distance of point (2,1, λ) from plane 3 x+5 y+ 4 z=11 is 2 √2 units.2022
- Find the value of λ if the following lines are perpendicular to each other: l_1: (1-x)/-3=(3 y-2)/(2 λ)=(z-3)/3; l_2: (x-1)/(3 λ)=(1-y)/1=(2 z-5)/32025
- The value of λ for which the angle between the lines r= i+ j+ k+p(2 i+ j+2 k) and r=(1+q) i+(1+q λ) j+(1+q) k is (π)/2 is:2023
- If a line makes an angle of (π)/4 with the positive directions of both x -axis and z -axis, then the angle which it makes with the positive direction…2024
- Assertion: If a line makes angles α, β, γ with positive direction of the coordinate axes, then sin^2 α+ sin^2 β+ sin^2 γ=2. Reason (R): The sum of…2023
- If the lines (x-3)/1=(1-y)/1=(z+2)/p and (2-x)/3=(y+1)/5=(z+56)/(2 p) are perpendicular to each other, then find the value(s) of p. OR Find the…2026
- Find the equation of the plane passing through points (2, 1, 0), (3, -2, -2) and (1, 1, -7). Also, obtain its distance from the origin. OR Find the…2022
CBSE Class 12 Mathematics past-paper question from the 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.