Using vectors find the area of triangle ABC with vertices A(1, 2, 3), B(2, -1, 4), and C(4, 5, -1).

Find the equation of the plane through the line of intersection of and perpendicular to the plane Hence find whether the plane thus obtained contains the line

OR

Find the vector and Cartesian equations of a line passing through (1, 2, -4) and perpendicular to the two lines and

For the curve, if x increases at the rate of 2 units/sec, then find the rate of change of the slope of the curve when

A metal box with a square base and vertical sides is to contain 1024 cm³. The material for the top and bottom costs ` 5 per cm<sup>2</sup> and the material for the sides costs ` 2.50 per cm². Find the least cost of the box.

If find Using solve the system of equation