Direction: Read the following text and answer the following questions on the basis of the same:
P_{1} : x + 3y – z = 0 and P_{2} : y + 2z = 0 are two intersecting planes. P_{3} is a plane passing through the point (2, 1, –1) and through the line of intersection of P_{1} and P_{2}.
Q. ______ is a point on P_{3}.
Direction: Read the following text and answer the following questions on the basis of the same:
P_{1} : x + 3y – z = 0 and P_{2} : y + 2z = 0 are two intersecting planes. P_{3} is a plane passing through the point (2, 1, –1) and through the line of intersection of P_{1} and P_{2}.
Q. Equation of P_{3} is _______.
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Direction: Read the following text and answer the following questions on the basis of the same:
P_{1} : x + 3y – z = 0 and P_{2} : y + 2z = 0 are two intersecting planes. P_{3} is a plane passing through the point (2, 1, –1) and through the line of intersection of P_{1} and P_{2}.
Q. The angle between P_{1} and P_{2} is _______.
Direction: Read the following text and answer the following questions on the basis of the same:
P_{1} : x + 3y – z = 0 and P_{2} : y + 2z = 0 are two intersecting planes. P_{3} is a plane passing through the point (2, 1, –1) and through the line of intersection of P_{1} and P_{2}.
Q. Equation of plane parallel to P_{3} and passing through (1, 2, 3) is _______.
Direction: Read the following text and answer the following questions on the basis of the same:
P_{1} : x + 3y – z = 0 and P_{2} : y + 2z = 0 are two intersecting planes. P_{3} is a plane passing through the point (2, 1, –1) and through the line of intersection of P_{1} and P_{2}.
Q. Distance of P_{3} from origin is _______ units.
Direction: Read the following text and answer the following questions on the basis of the same:
A mobile tower stands 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 3 cables from the points A, B and C such that it stands vertically on the ground. The top of the tower is at the point (2, 3, 1) as shown in the figure.
Q. The coordinates of the foot of the perpendicular drawn from the top of the tower to the ground are
Direction: Read the following text and answer the following questions on the basis of the same:
A mobile tower stands 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 3 cables from the points A, B and C such that it stands vertically on the ground. The top of the tower is at the point (2, 3, 1) as shown in the figure.
Q. The height of the tower from the ground is
Direction: Read the following text and answer the following questions on the basis of the same:
A mobile tower stands 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 3 cables from the points A, B and C such that it stands vertically on the ground. The top of the tower is at the point (2, 3, 1) as shown in the figure.
Q. The equation of the plane passing through the points A, B and C is
Direction: Read the following text and answer the following questions on the basis of the same:
A mobile tower stands 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 3 cables from the points A, B and C such that it stands vertically on the ground. The top of the tower is at the point (2, 3, 1) as shown in the figure.
Q. The equation of the perpendicular line drawn from the top of the tower to the ground is
Direction: Read the following text and answer the following questions on the basis of the same:
A mobile tower stands 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 3 cables from the points A, B and C such that it stands vertically on the ground. The top of the tower is at the point (2, 3, 1) as shown in the figure.
Q. The area of ΔABC is
Direction: Read the following text and answer the following questions on the basis of the same:
Consider the plane π_{1} : 2x – 3y + 4z + 9 = 0 and the point P(1, –2, 3). π_{1} is a plane parallel to π_{1} and containing the point P.
Q. The coordinates of A are _______.
Direction: Read the following text and answer the following questions on the basis of the same:
Consider the plane π_{1} : 2x – 3y + 4z + 9 = 0 and the point P(1, –2, 3). π_{1} is a plane parallel to π_{1} and containing the point P.
Q. Distance between π_{1} and π_{2} is _______ units.
Direction: Read the following text and answer the following questions on the basis of the same:
Consider the plane π_{1} : 2x – 3y + 4z + 9 = 0 and the point P(1, –2, 3). π_{1} is a plane parallel to π_{1} and containing the point P.
Q. Equation of π_{2} is _______.
Direction: Read the following text and answer the following questions on the basis of the same:
Consider the plane π_{1} : 2x – 3y + 4z + 9 = 0 and the point P(1, –2, 3). π_{1} is a plane parallel to π_{1} and containing the point P.
Q. A is the foot of perpendicular from π to π_{1}. Equation of PA is _______.
Direction: Read the following text and answer the following questions on the basis of the same:
Consider the plane π_{1} : 2x – 3y + 4z + 9 = 0 and the point P(1, –2, 3). π_{1} is a plane parallel to π_{1} and containing the point P.
Q. The image of π on π_{1} is _______.
204 videos288 docs139 tests

204 videos288 docs139 tests
