If a $$\Delta $$ABC has vertices A(–1, 7), B(–7, 1) and C(5, –5), then its orthocentre has coordinates :

The plane which bisects the line joining, the points (4, –2, 3) and (2, 4, –1) at right angles also passes through the point :

If the surface area of a cube is increasing at a rate of 3.6 cm²/sec, retaining its shape; then the rate of change of its volume (in cm³/sec), when the length of a side of the cube is 10 cm, is :

$$\mathop {\lim }\limits_{x \to a} {{{{\left( {a + 2x} \right)}^{{1 \over 3}}} - {{\left( {3x} \right)}^{{1 \over 3}}}} \over {{{\left( {3a + x} \right)}^{{1 \over 3}}} - {{\left( {4x} \right)}^{{1 \over 3}}}}}$$ ($$a$$ $$ \ne $$ 0) is equal to :