The equation of the line joining the points $(-3,4,11)$ and $(1,-2,7)$ is
- $\frac{x+3}{2}=\frac{y-4}{3}=\frac{z-11}{4}$
- $\frac{x+3}{-2}=\frac{y-4}{3}=\frac{z-11}{2}$
- $\frac{x+3}{-2}=\frac{y+4}{3}=\frac{z+11}{4}$
- $\frac{x+3}{2}=\frac{y+4}{-3}=\frac{z+11}{2}$
The Correct Option is B
Solution and Explanation
Top Questions on Three Dimensional Geometry
- Find the value of λ, if the points A(−1,−1,2), B(2,8,λ), C(3,11,6) are collinear.
- CBSE CLASS XII - 2025
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The vector equations of two lines are given as:
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Line 2: \[ \vec{r}_2 = 3\hat{i} + 3\hat{j} - 5\hat{k} + \mu(6\hat{i} + 9\hat{j} + 18\hat{k}) \]
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- CBSE Compartment XII - 2025
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Show that the following lines intersect. Also, find their point of intersection:
Line 1: \[ \frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4} \]
Line 2: \[ \frac{x - 4}{5} = \frac{y - 1}{2} = z \]
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Determine the vector equation of the line that passes through the point \( (1, 2, -3) \) and is perpendicular to both of the following lines:
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- CBSE CLASS XII - 2025
- CBSE Compartment XII - 2025
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In an experiment to determine the figure of merit of a galvanometer by half deflection method, a student constructed the following circuit. He applied a resistance of \( 520 \, \Omega \) in \( R \). When \( K_1 \) is closed and \( K_2 \) is open, the deflection observed in the galvanometer is 20 div. When \( K_1 \) is also closed and a resistance of \( 90 \, \Omega \) is removed in \( S \), the deflection becomes 13 div. The resistance of galvanometer is nearly:
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Concepts Used:
Three Dimensional Geometry
Mathematically, Geometry is one of the most important topics. The concepts of Geometry are derived w.r.t. the planes. So, Geometry is divided into three major categories based on its dimensions which are one-dimensional geometry, two-dimensional geometry, and three-dimensional geometry.
Direction Cosines and Direction Ratios of Line:
Consider a line L that is passing through the three-dimensional plane. Now, x,y and z are the axes of the plane and α,β, and γ are the three angles the line makes with these axes. These are commonly known as the direction angles of the plane. So, appropriately, we can say that cosα, cosβ, and cosγ are the direction cosines of the given line L.
