>
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 \[ \lim_{x \to 0} \frac{e^{a(x-1)} + 2\cos(bx) + e^{-x}(c - 1)}{x \cos x - \ln(1 + x)} = 2, \] Then the value of \( a^2 + b^2 + c^2 \) is:
JEE Main - 2026
Mathematics
Geometry
View Solution
If \( P(10, 2\sqrt{15}) \) 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
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
The locus of the point of intersection of tangents drawn to the circle \[ (x - 2)^2 + (y - 3)^2 = 16, \] which subtends an angle of \(120^\circ\), is:
JEE Main - 2026
Mathematics
Geometry
View Solution
View More Questions
Questions Asked in AP EAPCET exam
In a series LCR circuit, the voltages across the capacitor, resistor, and inductor are in the ratio 2:3:6. If the voltage of the source in the circuit is 240 V, then the voltage across the inductor is
AP EAPCET - 2025
Electromagnetic induction
View Solution
0.25 moles of $ \text{CH}_2\text{FCOOH} $ was dissolved in $ 0.5 \, \text{kg} $ of water. The depression in freezing point of the resultant solution was observed as $ 1^\circ \text{C} $. What is the van't Hoff factor? ($ K_f = 1.86 \, \text{K kg mol}^{-1} $)
AP EAPCET - 2025
Colligative Properties
View Solution
At $T(K)$, the vapor pressure of water is $x$ kPa. What is the vapor pressure (in kPa) of 1 molal solution containing non-volatile solute?
AP EAPCET - 2025
Colligative Properties
View Solution
At 300 K, vapour pressure of pure liquid A is 70 mm Hg. It forms an ideal solution with liquid B. Mole fraction of B = 0.2 and total vapour pressure of solution = 84 mm Hg. What is vapour pressure (in mm) of pure B?
AP EAPCET - 2025
Colligative Properties
View Solution
A 1% (w/v) aqueous solution of a certain solute is isotonic with a 3% (w/v) solution of glucose (molar mass 180 g mol$^{-1}$). The molar mass of solute (in g mol$^{-1}$) is
AP EAPCET - 2025
Colligative Properties
View Solution
View More Questions