Exams › JEE Main › Maths

Consider the three planes P1 : 3x + 15y + 21z = 9, P2 : x - 3y - z = 5, and P3 : 2x + 10y + 14z = 5 Then, which one of the following is true ? (1) P1 and P2 are parallel (2) P1 and P3 are parallel (3) P2 and P3 are parallel (4) P1, P2 and P3 are parallel

1. P1 and P2 are parallel
2. P1 and P3 are parallel
3. P2 and P3 are parallel
4. P1, P2 and P3 are parallel

Correct answer: P2 and P3 are parallel

Solution

P2 and P3 are parallel because their normal vectors are scalar multiples of each other, indicating that they have the same direction in space and will never intersect.

Related JEE Main Maths questions

• A line makes equal angles \(\alpha\), \(\beta\), and \(\gamma\) with the positive directions of the coordinate axes. If \(\theta\) satisfies \[ \cos\theta=\frac{\cos^2\alpha+\cos^2\beta+\cos^2\gamma}{\sin^2\alpha+\sin^2\beta+\sin^2\gamma}, \] then what is the value of \(\theta\)?
• Consider the following two statements: Statement 1: If \(A\), \(B\), and \(C\) are points with position vectors \(\mathbf{a}=2\hat{i}+\hat{j}+\hat{k}\), \(\mathbf{b}=3\hat{i}-\hat{j}+3\hat{k}\), and \(\mathbf{c}=\hat{i}+7\hat{j}-5\hat{k}\), then the figure \(OABC\) forms a tetrahedron. Statement 2: If the position vectors \(\mathbf{a}\), \(\mathbf{b}\), and \(\mathbf{c}\) of points \(A\), \(B\), and \(C\) are non-coplanar, then \(OABC\) is a tetrahedron, where \(O\) denotes the origin. Choose the correct option.
• Find the locus of a point whose sum of the squares of its perpendicular distances from the planes \(x+y+z=0\), \(x-z=0\), and \(x-2y+z=0\) equals 19.
• A moving plane always contains the fixed point \((1,2,3)\). The set of points that are the perpendicular projections of the origin onto this plane is described by
• The direction cosines \(l,m,n\) of one of the two lines satisfying the relations \(l-5m+3n=0\) and \(7l^2+5m^2-3n^2=0\) are
• A sphere is given by the equation \(x^2+y^2+z^2-10z=0\). If one endpoint of a diameter is \((-3,4,5)\), then what are the coordinates of the opposite endpoint?

⚔️ Practice JEE Main Maths free + battle 1v1 →