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I am Urvashi Arora Pursuing Ph.D. (Physics) from IIT(BHU), Varanasi. I love to learn the diverse areas of physics. I want to be a professor. I love to teach students also I have experience teaching graduate students.

Find an equation of the plane.

The plane through the origin and perpendicular to the vector $ \langle 1, -2, 5 \rangle $

The plane through the point $ (5, 3, 5) $ and with normal vector $ 2i + j - k $

The plane through the point $ (-1, \frac{1}{2}, 3) $ and with normal vector $ i + 4j + k $

The plane through the point $ (2, 0, 1) $ and perpendicular to the line $ x = 3t, y = 2 - t, z = 3 + 4t $

The plane through the point $ (1, -1, -1) $ and parallel to the plane $ 5x - y - z = 6 $

The plane through the point $ (3, -2, 8) $ and parallel to the plane $ z = x + y $