Find the equation of the plane through the point (2,3,4) and
1. Parallel,
2. Perpendicular,
3. intersecting ,
to the plane 5x-6y+7z=3.
Pleeease help me, I fail to understand or visualize them due to lack of good books.
1. Parallel,
2. Perpendicular,
3. intersecting ,
to the plane 5x-6y+7z=3.
Pleeease help me, I fail to understand or visualize them due to lack of good books.
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Question - 1:
i) Equations of parallel planes differ only in constant terms. So equation of a plane parallel to 5x-6y+7z = 3 is 5x - 6y + 7z = k
ii) Since this pass through (2,3,4), plugging this point, 10 - 18 + 21 = k; solving k = 13
Thus equation of the plane is: 5x - 6y + 7z = 13
For solving other two questions, we need one more point. You may verify and kindly provide one more point or data, which would enable us to solve.
i) Equations of parallel planes differ only in constant terms. So equation of a plane parallel to 5x-6y+7z = 3 is 5x - 6y + 7z = k
ii) Since this pass through (2,3,4), plugging this point, 10 - 18 + 21 = k; solving k = 13
Thus equation of the plane is: 5x - 6y + 7z = 13
For solving other two questions, we need one more point. You may verify and kindly provide one more point or data, which would enable us to solve.