Maths-
General
Easy

Question

The angle between the lines r left square bracket 2 C o s space theta plus 5 S i n space theta right square bracket equals 3 and r left square bracket 2 s i n space theta minus 5 C o s space theta right square bracket plus 4 equals 0 is

  1. 30 to the power of ring operator end exponent    
  2. 45 to the power of ring operator end exponent    
  3. 60 to the power of ring operator end exponent    
  4. 90 to the power of ring operator end exponent    

hintHint:

A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line. We have to find the angle between the lines r left square bracket 2 C o s space theta plus 5 S i n space theta right square bracket equals 3 and r left square bracket 2 s i n space theta minus 5 C o s space theta right square bracket plus 4 equals 0.

The correct answer is: 90 to the power of ring operator end exponent


    The intersection of two perpendicular lines results in the formation of the cartesian plane, a two-dimensional coordinate plane. The X-axis is the horizontal line, and the Y-axis is the vertical line. The Cartesian coordinate point (x, y) indicates that the distance from the origin is x in the horizontal direction and y in the vertical direction.
    Now the given lines are:
    r left square bracket 2 C o s space theta plus 5 S i n space theta right square bracket equals 3 and r left square bracket 2 s i n space theta minus 5 C o s space theta right square bracket plus 4 equals 0 
    The cartesian form will be:

    253
    2− 54

    Slopes of these lines are 5/2 and 2/5
    Here, we can say that the product of slopes is 1
    Hence, these lines are perpendicular so the angles between them is 90 degrees.

    Here we used the concept of cartesian lines and some trigonometric terms to solve. With the help of slope we identified the angle between them. Hence, these lines are perpendicular so the angle between them is 90 degrees.

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