Let \((\alpha, \beta, \gamma)\) \(\text{ be the image of the point }\) \(P(3, 3, 5) \text{ in the plane } 2x + y - 3z = 6\). \(\text{ Then } \alpha + \beta + \gamma \text{ is equal to:}\)
Let \((\alpha, \beta, \gamma)\) \(\text{ be the image of the point }\) \(P(3, 3, 5) \text{ in the plane } 2x + y - 3z = 6\). \(\text{ Then } \alpha + \beta + \gamma \text{ is equal to:}\)
Approach Solution - 1
The correct answer is : 10
\(\frac{x-2}{2}=\frac{y-3}{1}=\frac{z-5}{-3}=-2\frac{(-14)}{14}\)
\(\Rightarrow x=6,y=5,z=-1\)
\(\therefore \alpha=6,\beta=5,\gamma=-1\)
\(\alpha+\beta+\gamma = 6+5-1=10\)
Approach Solution -2
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Concepts Used:
Tangents and Normals
- A tangent at a degree on the curve could be a straight line that touches the curve at that time and whose slope is up to the derivative of the curve at that point. From the definition, you'll be able to deduce the way to realize the equation of the tangent to the curve at any point.
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m×n = -1
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Diagram Explaining Tangents and Normal:
