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The acute angle between the lines y = 2x and y = - 2x is
  • a)
    Both are equal
  • b)
    greater than 600
  • c)
    less than 600
  • d)
    none of these
Correct answer is option 'C'. Can you explain this answer?
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The acute angle between the lines y = 2x and y = - 2x isa)Both are equ...
To find the acute angle between two lines, we can use the formula:

θ = tan^(-1) |(m1 - m2) / (1 + m1 * m2)|

where m1 and m2 are the slopes of the two lines.

Given the equations of the lines as y = 2x and y = -2x, we can determine their slopes:

m1 = slope of y = 2x = 2
m2 = slope of y = -2x = -2

Substituting these values into the formula, we have:

θ = tan^(-1) |(2 - (-2)) / (1 + 2 * (-2))|
= tan^(-1) |4 / (1 - 4)|
= tan^(-1) |-4 / (-3)|
= tan^(-1) (4/3)

Now, let's calculate the value of θ using a calculator:

θ ≈ 53.13°

Since the question asks for the acute angle between the lines, we consider the positive value of the angle. Therefore, the acute angle between the lines y = 2x and y = -2x is approximately 53.13°.

Hence, the correct answer is option C: The acute angle between the lines y = 2x and y = -2x is less than 60°.
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The acute angle between the lines y = 2x and y = - 2x isa)Both are equalb)greater than600c)less than600d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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