GATE EE 2002 | Vector Calculus Question 20 | Engineering Mathematics

GATE EE 2002

MCQ (Single Correct Answer)

-0.3

Given a vector field $${\overrightarrow F ,}$$ the divergence theorem states that

$$\int\limits_s {\overrightarrow F .d\overrightarrow s = \int\limits_v \nabla .\overrightarrow F \,dv} $$

$$\int\limits_s {\overrightarrow F .d\overrightarrow s = \int\limits_v \nabla \times \overrightarrow F \,dv} $$

$$\int\limits_s {\overrightarrow F \times d\overrightarrow s = \int\limits_v \nabla .\overrightarrow F \,dv} $$

$$\int\limits_s {\overrightarrow F \times d\overrightarrow s = \int\limits_v \nabla \times \overrightarrow F \,dv} $$

GATE EE 1994

MCQ (Single Correct Answer)

-0.3

The directional derivative of $$f\left( {x,y} \right) = 2{x^2} + 3{y^2} + {z^2}\,\,$$ at point $$P\left( {2,1,3} \right)\,\,$$ in the direction of the vector $$\,\,a = \overrightarrow i - 2\overrightarrow k \,\,$$ is

$$4/\sqrt 5 $$

$$-$$ $$4/\sqrt 5 $$

$$\sqrt 5 /4$$

$$-$$ $$\sqrt 5 /4$$

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