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Find the equation of the plane through t...

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.

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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 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 .