The $$x$$-intercept of a plane $$\pi$$ passing through the point $$(1,1,1)$$ is $$\frac{5}{2}$$ and the perpendicular distance from the origin to the plane $$\pi$$ is $$\frac{5}{7}$$. If the $$y$$-intercept of the plane $$\pi$$ is negative and the $$z$$-intercept is positive, then its $$y$$-intercept is

The equation of the plane passing through $$3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}$$ and parallel to the vectors $$2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ is

The direction cosines of the line joining the points $$(-2,4,-5)$$ and $$(1,2,3)$$ are

The points (2, 3, 4), ($$-$$1, $$-$$2, 1) and (5, 8, 7) are