>
Exams
>
Mathematics
>
Geometry
>
if the four points 6 2 4 1 3 5 1 2 3 and 6 k 2 are
Question:
If the four points (6,2,4), (1,3,5), (1,-2,3), and (6,k,2) are coplanar, then \(k =\)
Show Hint
To test coplanarity of 4 points, use scalar triple product of vectors = 0.
AP EAPCET - 2025
AP EAPCET
Updated On:
Jun 4, 2025
-5
4
-3
1
Hide Solution
Verified By Collegedunia
The Correct Option is
C
Solution and Explanation
Check coplanarity using scalar triple product = 0. Take three vectors formed from one base point and equate volume expression to zero.
Download Solution in PDF
Was this answer helpful?
0
0
Top Questions on Geometry
If \( P(10, 2\sqrt{15}) \) lies on the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) and the length of the latus rectum is 8, then the square of the area of \( \Delta PS_1S_2 \) is [where \( S_1 \) and \( S_2 \) are the foci of the hyperbola].
JEE Main - 2026
Mathematics
Geometry
View Solution
A rectangle is formed by the lines \( x = 0,\ y = 0,\ x = 3,\ y = 4 \). A line perpendicular to \( 3x + 4y + 6 = 0 \) divides the rectangle into two equal parts. Then the distance of the line from the point \( \left(-1,\frac{3}{2}\right) \) is:
JEE Main - 2026
Mathematics
Geometry
View Solution
If \[ \lim_{x \to 0} \frac{e^{a(x-1)} + 2\cos(bx) + e^{-x}(c - 1)}{x \cos x - \ln(1 + x)} = 2, \] Then the value of \( a^2 + b^2 + c^2 \) is:
JEE Main - 2026
Mathematics
Geometry
View Solution
If \( \cos(\alpha + \beta) = -\frac{1}{10} \) and \( \sin(\alpha - \beta) = \frac{3}{8} \), where \[ 0<\alpha<\frac{\pi}{3} \quad \text{and} \quad 0<\beta<\frac{\pi}{4}, \] and \[ \tan(2\alpha) = \frac{3\left(1 - \sqrt{55}\right)}{\sqrt{11} \left(s + \sqrt{5}\right)}, \] and \( r, s \in \mathbb{N} \), then \( r^2 + s \) is:
JEE Main - 2026
Mathematics
Geometry
View Solution
If \( O \) is the vertex of the parabola \( x^2 = 4y \), \( Q \) is a point on the parabola. If \( C \) is the locus of a point which divides \( OQ \) in the ratio \( 2:3 \), then the equation of the chord of \( C \) which is bisected at the point \( (1,2) \) is:
JEE Main - 2026
Mathematics
Geometry
View Solution
View More Questions
Questions Asked in AP EAPCET exam
The voltage gains of two amplifiers connected in series are 8 and 12.5. If the voltage of the input signal is 200 \(\mu V\), then the voltage of the output signal is
AP EAPCET - 2025
Transistors
View Solution
If a straight current-carrying wire of linear density $0.12~\text{kg/m
$ is suspended in mid-air by a uniform horizontal magnetic field of $0.5~\text{T}$ normal to the length of the wire, then the current through the wire is (Neglect earth’s magnetic field)}
AP EAPCET - 2025
Magnetism and matter
View Solution
The equations for the displacements of two particles in simple harmonic motion are \( y_1 = 0.1\sin\left(100\pi t + \frac{\pi}{3}\right) \) and \( y_2 = 0.1\cos(\pi t) \) respectively. The phase difference between the velocities of the two particles at a time \( t = 0 \) is
AP EAPCET - 2025
Waves and Oscillations
View Solution
If the velocity at the maximum height of a projectile projected at an angle of \(45^\circ\) is \(20 \, \text{m/s}\), then the maximum height reached by the projectile is:
AP EAPCET - 2025
Rotational motion
View Solution
Steam at \( 100^\circ \)C is passed into \( 114 \) g of water at \( 30^\circ \)C. The mass of water present in the mixture when the temperature of the water becomes \( 70^\circ \)C is:
AP EAPCET - 2025
Thermodynamics
View Solution
View More Questions