181.Find the vector equation of the line through the origin which is perpendicular to the plane
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182.Find the vector and cartesian equations of the planes: that passes through the point (1, 0, – 2) and the normal to the plane is .
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183.Find the vector and cartesian equations of the planes: that passes through the point (1, 4, 6) and the normal vector to the plane is .
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Long Answer Type
184.Find the vector equation of the line passing through the point (3, 1, 2) and perpendicular to the plane Find also the point of intersection of this line and plane.
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Short Answer Type
185.Find the angle between the two planes 3 x – 6 y + 2 z = 7 and 2 x + 2 y – 2 z = 5.
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186.Find the angle between the two planes 2 x + y – 2 z = 5 and 3x – 6 y – 2 z = 7 using vector method.
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187.Find the angle between the planes whose vector equations are
188.Find the angle between the planes whose vector equations are
The equation of the two planes are Let θ be the angle between the planes.
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189.Find the angle between the planes
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190.In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them: 7x + 5y + 6z + 30 = 0 and 3x – y – 10z + 4 = 0
Short Answer Type
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Long Answer Type
Find also the point of intersection of this line and plane.
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