Question:
If \(\vec{r}=4\hat{i}+2\hat{j}+7\hat{k}+\lambda (3\hat{i}-5\hat{k})\) is the vector equation of the line passing through \((7,2,2)\), where \(\lambda\) is parameter, then the value of \(\lambda\) is...
If \(\vec{r}=4\hat{i}+2\hat{j}+7\hat{k}+\lambda (3\hat{i}-5\hat{k})\) is the vector equation of the line passing through \((7,2,2)\), where \(\lambda\) is parameter, then the value of \(\lambda\) is...
Show Hint
Equate the position vector of the given point with the line equation and compare components.
Updated On: Nov 12, 2026
- \(-1\)
- \(2\)
- \(-2\)
- \(1\)
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
The point \((7,2,2)\) has position vector \(7\hat{i}+2\hat{j}+2\hat{k}\). It lies on the line for some \(\lambda\).
Step 2: Equate
\(4\hat{i}+2\hat{j}+7\hat{k}+\lambda(3\hat{i}-5\hat{k})=7\hat{i}+2\hat{j}+2\hat{k}\).
Step 3: Compare Components
\(\hat{i}\): \(4+3\lambda=7\Rightarrow\lambda=1\).
\(\hat{k}\): \(7-5\lambda=2\Rightarrow\lambda=1\).
Final Answer:
The value of lambda is 1. \[ \boxed{\text{(D) }1} \]
The point \((7,2,2)\) has position vector \(7\hat{i}+2\hat{j}+2\hat{k}\). It lies on the line for some \(\lambda\).
Step 2: Equate
\(4\hat{i}+2\hat{j}+7\hat{k}+\lambda(3\hat{i}-5\hat{k})=7\hat{i}+2\hat{j}+2\hat{k}\).
Step 3: Compare Components
\(\hat{i}\): \(4+3\lambda=7\Rightarrow\lambda=1\).
\(\hat{k}\): \(7-5\lambda=2\Rightarrow\lambda=1\).
Final Answer:
The value of lambda is 1. \[ \boxed{\text{(D) }1} \]
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 Equation of a Line in Space Questions
- Identify the co-ordinates of the point where the line joining \( (1,1,1) \) and \( (2,2,2) \) intersects the plane \( x+y+z=9 \).
- If the lines $\frac{x-k}{2} = \frac{y+1}{3} = \frac{z-1}{4}$ and $\frac{x-3}{1} = \frac{y-\frac{9}{2{2} = \frac{z}{1}$ intersect, then the value of k is
- If the Cartesian equation of a line is $6x-2=3y+1=2z-2$, then the vector equation of the line is
- The equation of a line passing through the point $(-1, 2, 3)$ and perpendicular to the lines $\frac{x}{2} = \frac{y-1}{-3} = \frac{z+2}{-2}$ and $\frac{x+3}{-1} = \frac{y+3}{2} = \frac{z-1}{3}$ is
- The number of solutions of \(16^{\sin^2 x} + 16^{\cos^2 x} = 10\) in \(0 \le x \le 2\pi\) are
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