✓ Board-verified
Mathematics · 2024 · 1 mark
Three Dimensional GeometryDirection Cosines and Direction Ratios of a Line1 markAnalyseassertion reason
CBSE 2024 · Region 1 · Set 1 · Q20
Assertion (A): A line in space cannot be drawn perpendicular to x, y and z axes simultaneously. Reason ( R ): For any line making angles, α, β, γ…
Assertion (A) : A line in space cannot be drawn perpendicular to $\displaystyle \mathrm{x}, \mathrm{y}$ and z axes simultaneously. Reason ( $\displaystyle R$ ) : For any line making angles, $\displaystyle \alpha, \beta, \gamma$ with the positive directions of $\displaystyle \mathrm{x}, \mathrm{y}$ and $\displaystyle z$ axes respectively, $\displaystyle \cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1$.
Official answer
(A)
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
All Three Dimensional Geometry questions2024 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 2024 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.