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.
The equation of plane is ....(1) Vector along the normal to the plane is Now required line passes through point (3, 1, 2) with position vector and is parallel to the vector ...(2) ∴ equation of line is Now line (2) meets plane (1) when Putting this value of λ in (2), we get the position vector of the point of intersection of (1) and (2) as
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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
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188.Find the angle between the planes whose vector equations are
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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.
....(1)
and is parallel to the vector 
...(2)
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