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प्रश्न
Choose correct alternatives :
The equation of the plane in which the line `(x - 5)/(4) = (y - 7)/(4) = (z + 3)/(-5) and (x - 8)/(7) = (y - 4)/(1) = (z - 5)/(3)` lie, is
पर्याय
17x – 47y – 24z + 172 = 0
17x + 47y – 24z + 172 = 0
17x + 47y + 24z + 172 = 0
17x – 47y + 24z + 172 = 0
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उत्तर
17x – 47y – 24z + 172 = 0
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संबंधित प्रश्न
Find the perpendicular distance of the point (1, 0, 0) from the line `(x - 1)/(2) = (y + 1)/(-3) = (z + 10)/(8)` Also find the co-ordinates of the foot of the perpendicular.
Find the perpendicular distance of the origin from the plane 6x – 2y + 3z – 7 = 0.
Find the coordinates of the foot of the perpendicular drawn from the origin to the plane 2x + 6y – 3z = 63.
Reduce the equation `bar"r".(3hat"i" + 4hat"j" + 12hat"k")` to normal form and hence find
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(ii) direction cosines of the normal.
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Solve the following :
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Find the coordinates of the foot of the perpendicular drawn from the origin to the plane 2x + 3y + 6z = 49.
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Reduce the equation `bar"r".(6hat"i" + 8hat"j" + 24hat"k")` = 13 normal form and hence find
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(ii) direction cosines of the normal.
The equation of X axis is ______
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The coordinates of the foot of perpendicular drawn from the origin to the plane 2x + y − 2z = 18 are ______
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Find direction cosines of the normal to the plane `bar"r"*(3hat"i" + 4hat"k")` = 5
Find the vector equation of a plane at a distance 6 units from the origin and to which vector `2hat"i" - hat"j" + 2hat"k"` is normal
Find the vector equation of the plane which bisects the segment joining A(2, 3, 6) and B(4, 3, −2) at right angles
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Equation of the plane passing through A(-2, 2, 2), B(2, -2, -2) and perpendicular to x + 2y - 3z = 7 is ______
The equation of a plane containing the line of intersection of the planes 2x - y - 4 = 0 and y + 2z - 4 = 0 and passing through the point (1, 1, 0) is ______
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A mobile tower is situated at the top of a hill. Consider the surface on which the tower stands as a plane having points A(1, 0, 2), B(3, –1, 1) and C(1, 2, 1) on it. The mobile tower is tied with three cables from the points A, B and C such that it stands vertically on the ground. The top of the tower is at point P(2, 3, 1) as shown in the figure below. The foot of the perpendicular from the point P on the plane is at the point `Q(43/29, 77/29, 9/29)`.
Answer the following questions.
- Find the equation of the plane containing the points A, B and C.
- Find the equation of the line PQ.
- Calculate the height of the tower.
If the plane \[\frac{x}{3}+\frac{y}{2}-\frac{z}{4}=1\] cuts the coordinate axes at points A, B and C, then the area of the X triangle ABC is
