Question:
The distance of the point $(-3, 2, 3)$ from the line passing through $(4, 6, -2)$ and having direction ratios $-1, 2, 3$ is ________ units.
The distance of the point $(-3, 2, 3)$ from the line passing through $(4, 6, -2)$ and having direction ratios $-1, 2, 3$ is ________ units.
Show Hint
Use cross product formula for shortest distance.
Updated On: Apr 26, 2026
- $2\sqrt{17}$
- $4\sqrt{17}$
- $2\sqrt{19}$
- $4\sqrt{19}$
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Concept:
Distance from point to line: \[ d = \frac{|(\vec{AP} \times \vec{d})|}{|\vec{d}|} \] Step 1: Find AP. \[ (-3-4, 2-6, 3+2) = (-7,-4,5) \]
Step 2: Cross product. \[ |AP \times d| = 2\sqrt{17} \]
Step 3: Conclusion. Distance = $2\sqrt{17}$
Distance from point to line: \[ d = \frac{|(\vec{AP} \times \vec{d})|}{|\vec{d}|} \] Step 1: Find AP. \[ (-3-4, 2-6, 3+2) = (-7,-4,5) \]
Step 2: Cross product. \[ |AP \times d| = 2\sqrt{17} \]
Step 3: Conclusion. Distance = $2\sqrt{17}$
Was this answer helpful?
0
0
Top MHT CET Mathematics Questions
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- If $\int\frac{f\left(x\right)}{log \left(sin\,x\right)}dx = log\left[log\,sin\,x\right]+c$ then $f\left(x\right)=$
- If $\int\limits^{K}_0 \frac{dx}{2 + 18 x^2} = \frac{\pi}{24}$, then the value of K is
- If $\int^{\pi/2}_{0} \log\cos x dx =\frac{\pi}{2} \log\left(\frac{1}{2}\right)$ then $ \int^{\pi/2}_{0} \log\sec x dx = $
- The point on the curve $y = \sqrt{x - 1}$ where the tangent is perpendicular to the line $2x + y - 5 = 0 $ is
View More Questions
Top MHT CET Some Properties of Definite Integrals Questions
- Evaluate the integral \[ \int_{0}^{\pi} \frac{x \cos x \sin x}{\cos^3 x + \cos x}\,dx \]
- Evaluate the integral: \[ \int_{-1}^{1} \left[ \sqrt{1 + x + x^2} - \sqrt{1 - x + x^2} \right] dx \]
- Evaluate \( \int_0^{\frac{\pi}{2}} \left( e^{\sin x} - e^{\cos x} \right) \, dx \)
- If \( \int_{0}^{1} (5x^2 - 3x + k) \, dx = 0 \), then \( k = \)
- Evaluate \( \displaystyle \int_{-\pi}^{\pi} \frac{2x}{1+\cos^2 x}\,dx \)
View More Questions
Top MHT CET Questions
- During r- DNA technology, which one of the following enzymes is used for cleaving DNA molecule ?
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- The temperature of $32^{\circ}C$ is equivalent to
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- The heat of formation of water is $ 260\, kJ $ . How much $ H_2O $ is decomposed by $ 130\, kJ $ of heat ?
View More Questions