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Find the vector equation of the plane wh...

Find the vector equation of the plane which contains the line of intersection of the planes `vecr.(hat(i) + 2hat(j) + 3hat(k)) - 4 = 0`  and `vecr.(2hat(i) + hat(j) - hat(k)) + 5 = 0`  and which is perpendicular to the plane `vecr.(5hat(i) + 3hat(j) - 6hat(k)) + 8 = 0`.

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The correct Answer is:
`r.(33hat(i) + 45hat(j) + 50 hat(k)) = 41`
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Find the vector equation of the plane passing through the intersection of the planes vecr.(hat(i) + hat(j) + hat(k)) = 6 and vecr.(2hat(i) + 3hat(j) + 4hat(k))= - 5 and the point (1, 1, 1).

Find the equation of the plane through the intersection of the planes vecr.(hat(i) + 3hat(j)) - 6 = 0 and vecr.(3hat(i) - hat(j) - 4hat(k)) = 0 , whose perpendicular distance from origin is unity.

Find the angle between the planes whose vector equations are r.(2hat(i) + 2hat(j) - 3hat(k)) = 5 and r.(3hat(i) - 3hat(j) + 5hat(k)) = 3 .