COMEDK · Maths · 34. Three Dimensional Geometry
The measure of the angle between the lines \(x=k+1, \quad y=2 k-1, \quad z=2 k+3, \quad k \in R \quad\) and \(\quad \dfrac{x-1}{2}=\dfrac{y+1}{1}=\dfrac{z-1}{-2}\) is
- A \(\sin ^{-1}\left(\dfrac{4}{3}\right)\)
- B \(\cos ^{-1}\left(\dfrac{4}{9}\right)\)
- C \(\sin ^{-1}\left(\dfrac{\sqrt{5}}{3}\right)\)
- D \(\dfrac{\pi}{2}\)
Answer & Solution
Correct Answer
(D) \(\dfrac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
The first line is given by \(x = k+1\), \(y = 2k-1\), \(z = 2k+3\). This can be written in symmetric form as \(\dfrac{x-1}{1} = \dfrac{y+1}{2} = \dfrac{z-3}{2} = k\). The direction vector of this line is \(\vec{v_1} = \hat{i} + 2\hat{j} + 2\hat{k}\). The second line is given by…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The circle \(x^2+y^2+3 x-y+2=0\) cuts an intercept on \(X\)-axis of lengthCOMEDK 2023 Easy
- If \(f(x)+2 f(1-x)=x \forall x \in R\), then \(f(x)\) is equal toCOMEDK 2024 Medium
- A line makes the same angle \(\theta\) with each of the \(x\) and \(z\)-axes. If the angle \(\beta\), which it makes with the \(y\)-axis is such that \(\sin ^2 \beta=3 \sin ^2 \theta\), then \(\cos ^2 \theta\) equalsCOMEDK 2024 Medium
- The sum of three numbers is 20 .
If we multiply the first number by 2 and add the second number to the result, and subtract the third number, we get 23 .
By adding second and third numbers to three times the first number, we get 46.
The above situation can be represented in matrix form as \(A X=B\) then the value of determinant formed by the cofactors of matrix A isCOMEDK 2025 Medium - If \(1, \omega, \omega^{2}\) are the cube roots of unity, then \((\mathbf{i}+\omega)\left(\mathbf{i}+\omega^{2}\right)\left(\mathbf{i}+w^{4}\right)\left(\mathbf{i}+\omega^{8}\right)\) is equal ioCOMEDK 2020 Medium
- Number of terms in the binomial expansion of \((x+a)^{53}+(x-a)^{53}\) isCOMEDK 2021 Easy
More PYQs from COMEDK
- In the case of an inductorCOMEDK 2023 Easy
- The reaction taking place in a galvanic cell is as given
\(\mathrm{A}(\mathrm{s})+\mathrm{B}^{2+}\left(\mathrm{1} \mathrm{1} \mathrm{1 0} \mathrm{0}^{-\mathrm{M}} \mathrm{M}\right) \rightarrow \mathrm{B}_{(\mathrm{s})}+\mathrm{A}^{2+}(0.1 \mathrm{M}).\)
The emf of the cell is \(+2.651 \mathrm{~V}\). If the standard emf of the cell is \(+2.71 \mathrm{~V}\), what is the value of \(\mathrm{X}\) ?COMEDK 2023 Medium - A small hollow vessel which has a small circular hole of radius r in its base, is immersed in a tank of oil of density \(\rho\) and surface tension T. The oil will penetrate into the vessel at a depth ofCOMEDK 2026 Medium
- From among the following, identify the compound which forms two moles of a ketone on ozonolysis.
[A] 2,3-Dimethylbutane.
[B] 3-Methyl-1-pentene.
[C] 2,3-Dimethyl-2-butene.
[D] 2-Methyl-2-pentane.COMEDK 2023 Medium - A and B are two independent events. The probability of their simultaneous occurrence is \(\dfrac{1}{8}\) and the probability that neither of them occurs is \(\dfrac{3}{8}\). Then their individual probabilities areCOMEDK 2024 Medium
- A plot of kinetic energy of emitted photoelectrons from a metal versus the frequency of incident radiation gives a straight line, the intercept of which
A. Depends on the nature of the metal used
B. Depends on the intensity of radiation
C. Depends both on the intensity and the nature of metal used
D. Is a constant and is same for all metals which is independent of the intensity of Incident radiationCOMEDK 2025 Easy