Question

find the direction ratios of the line 2x+1=3-2y=4z+5​

Answer 1

2/3,-2/3,1/3

Step-by-step explanation:

explanation is in pic

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Answer 2

Given:

• Equation of the line = 2x+1 = 3-2y = 4z+5

To Find:

• The direction ratios of the line.

Solution:

• Consider the equation, 2x+1 = 3-2y = 4z+5 → (1)
• Taking respective numbers common from equation (1) we get,
• ⇒ 2(x+1/2) = -2(y-3/2) = 4(z+5/4) → (2)
• ⇒ $\frac{x+\frac{1}{2} }{\frac{1}{2} } = \frac{y-\frac{3}{2} }{\frac{-1}{2} } = \frac{z+\frac{5}{4} }{\frac{1}{4} }$  
• The equation (2) is in the form of $\frac{x-x_1}{a}=\frac{y-y_1}{b} =\frac{z-z_1}{c}$
• Where, a, b, and, c are the direction ratios.
• ∴ a = 1/2, b = -1/2 and c = 1/4 ( They are the direction ratios)

∴ The direction ratios are 1/2, -1/2, and 1/4