Chapter 6 Line and Plane Ex 6.4 Solutions

The acute angle θ between the planes = d1 and = d2 is given by

The acute angle θ between the line and the plane = d is given by

= 2(-1) + 6(2) + 3(-1) = -2 + 12 – 3 = 7 ∴ Hence, the given lines are coplanar. The plane determined by these lines is given by ∴ i.e. Hence, the given lines are coplanar and the equation of the plane determined by these lines is = 7

The distance of the point A() from the plane is given by d = …(1) Here, , , p = 21 ∴ = = (4)(2) + (-3)(3) + (1)(-6) = 8 – 9 – 6 = -7 Also, = 7 ∴ from (1), the required distance = = 4units

The distance of the point (x1, y1, z1) from the plane ax + by + cz + d = 0 is ∴ the distance of the point (1, 1, -1) from the plane 3x + 4y – 12z + 20 = 0 is = = = 3units