KCET · Maths · Straight Lines
The locus represented by \( x y+y z=0 \) is
- A A pair of perpendicular lines
- B A pair of parallel lines
- C A pair of parallel planes
- D A pair of perpendicular planes
Answer & Solution
Correct Answer
(D) A pair of perpendicular planes
Step-by-step Solution
Detailed explanation
Given the locus
\[
\begin{array}{l}
x y+y z=0 \\
\Rightarrow y(x+z)=0 \\
\Rightarrow \vec{y} \cdot(\vec{x}+\vec{z})=0
\end{array}
\]
Therefore, it represents a pair of perpendicular planes.
\[
\begin{array}{l}
x y+y z=0 \\
\Rightarrow y(x+z)=0 \\
\Rightarrow \vec{y} \cdot(\vec{x}+\vec{z})=0
\end{array}
\]
Therefore, it represents a pair of perpendicular planes.
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
- If \( |x-2| \leq 1 \), thenKCET 2017 Hard
- Which one of the following is possible?KCET 2009 Easy
- The area of the region bounded by the curve \( y=x^{2} \) and the line \( y=16 \) isKCET 2017 Medium
- A simple graph contains 24 edges. Degree of each vertex is 3 . The number of vertices isKCET 2010 Easy
- \( \int \frac{(x+3) e^{x}}{(x+4)^{2}} d x \) is eqal toKCET 2017 Medium
- The point \((1,-3,4)\) lies in the octantKCET 2020 Medium
More PYQs from KCET
- If \( f(x)=\sin ^{-1}\left[\frac{2^{x+1}}{1+4^{x}}\right] \), then \( f^{\prime}(0)= \)KCET 2019 Hard
- A thin uniform rectangular plate of mass \(2 \mathrm{~kg}\) is placed in \(x y\)-plane as shown in figure. The moment of inertial about \(x\)-axis is \(I_{x}=0.2 \mathrm{kgm}^{2}\) and the moment of inertia about \(Y\)-axis is \(I_{y}=0.3 \mathrm{kgm}^{2}\). The radius of gyration of the plate about the axis passing through \(O\) and perpendicular to the plane of the plate is
KCET 2020 Easy - The magnetic field at the center of a current carrying loop of radius \( 0.1 \mathrm{~m} \) is \( 5 \sqrt{5} \) times that at
a point along its axis. The distance of this point from the centre of the loop isKCET 2017 Easy - Identify the incorrect statementKCET 2024 Easy
- Two slabs are of the thicknesses \(d_{1}\) and \(d_{2}\). Their thermal conductivities are \(\mathrm{K}_{1}\) and \(\mathrm{K}_{2}\) respectively. They are in series. The free ends of the combination of these two slabs are kept at temperatures \(\theta_{1}\) and \(\theta_{2}\). Assume \(\theta_{1}>\theta_{2}\). The temperature \(\theta\) of their common junction isKCET 2010 Hard
- If the refractive index from air to glass is \(\frac{3}{2}\) and that from air to water is \(\frac{4}{3}\), then the ratio of focal lengths of a glass lens in water and in air isKCET 2021 Medium