Practice Symmetric Form - 5.3 | 6. Three Dimensional Geometry | ICSE 12 Mathematics
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Symmetric Form

5.3 - Symmetric Form

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Practice Questions

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Question 1 Easy

Write the symmetric form for the line passing through (1, 2, 3) with direction ratios (4, 5, 6).

💡 Hint: Use the structure \\( \\frac{x - x_1}{a} = \\frac{y - y_1}{b} = \\frac{z - z_1}{c} \\).

Question 2 Easy

What are the direction ratios of the line given by the symmetric form: (x-1)/3 = (y-4)/2 = (z-5)/1?

💡 Hint: Identify the numbers in the denominator of the ratios.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the Symmetric Form of a line in 3D?

A representation using midpoints
An equation combining coordinates and direction ratios
A method to find angles alone

💡 Hint: Think about what ratios represent in relations to lines.

Question 2

True or False: The Symmetric Form can be used to determine if two lines are parallel.

True
False

💡 Hint: What do direction ratios tell us about lines?

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Identify if the following lines represented by their symmetric forms intersect: A: (x-1)/2 = (y+3)/3 = (z-4)/1 and B: (x+2)/2 = (y-5)/-1 = (z+1)/0.

💡 Hint: Align the equations correctly.

Challenge 2 Hard

Determine the angle between two lines expressed in symmetric forms: A: (x-1)/1 = (y-2)/2 = (z-3)/-3 and B: (x+3)/3 = (y-1)/1 = (z+2)/1.

💡 Hint: Remember the angle can be determined using cosines via direction ratios.

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