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The co-ordinates of the point where the line joining the points (2, –3, 1), (3, –4, –5) cuts the plane 2x + y + z = 7 are
  • a)
    (2,1,0)
  • b)
    (3,2,5)
  • c)
    (1,–2,7)
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The co-ordinates of the point where the line joiningthe points (2, &nd...
The co-ordinates of the point where the line joining the points (2, 3) and (-4, 1) intersects the x-axis can be found by setting the y-coordinate of the point equal to 0.

The equation of the line can be found using the slope-intercept form: y = mx + b, where m is the slope of the line and b is the y-intercept.

The slope (m) can be found using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Using the given points (2, 3) and (-4, 1), we can calculate the slope:

m = (1 - 3) / (-4 - 2)
= -2 / -6
= 1/3

Now we can substitute the slope (m) and one of the points (2, 3) into the slope-intercept form to find the y-intercept (b):

3 = (1/3)(2) + b
3 = 2/3 + b
b = 3 - 2/3
b = 7/3

The equation of the line is y = (1/3)x + 7/3.

To find the x-coordinate of the point where the line intersects the x-axis, we set y = 0:

0 = (1/3)x + 7/3
(1/3)x = -7/3
x = (-7/3)(3/1)
x = -7

Therefore, the point where the line intersects the x-axis is (-7, 0).
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The co-ordinates of the point where the line joiningthe points (2, –3, 1), (3, –4, –5) cuts the plane2x + y + z = 7 area)(2,1,0)b)(3,2,5)c)(1,–2,7)d)None of theseCorrect answer is option 'C'. Can you explain this answer?
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