GATE ME 2008 | Vector Calculus Question 25 | Engineering Mathematics

The directional derivative of the scalar function $$f(x, y, z)$$$$ = {x^2} + 2{y^2} + z\,\,$$ at the point $$P = \left( {1,1,2} \right)$$ in the direction of the vector $$\,\overrightarrow a = 3\widehat i - 4\widehat j\,\,$$ is

$$-4$$

$$-2$$

$$-1$$

$$1$$

GATE ME 2007

MCQ (Single Correct Answer)

-0.6

The area of a triangle formed by the tips of vectors $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ is

$${1 \over 2}\left( {\overrightarrow a - \overrightarrow b } \right) \bullet \left( {\overrightarrow a - \overrightarrow c } \right)$$

$${1 \over 2}\left| {\left( {\overrightarrow a - \overrightarrow b } \right) \times \left( {\overrightarrow a - \overrightarrow c } \right)} \right|$$

$${1 \over 2}\left| {\overrightarrow a \times \overrightarrow b \times \overrightarrow c } \right|$$

$${1 \over 2}\left( {\overrightarrow a \times \overrightarrow b } \right) \bullet \overrightarrow c $$

Questions Asked from Marks 2

GATE ME 2025 (1) GATE ME 2022 Set 1 (1) GATE ME 2017 Set 2 (1) GATE ME 2017 Set 1 (1) GATE ME 2016 Set 3 (1) GATE ME 2016 Set 2 (1) GATE ME 2015 Set 2 (1) GATE ME 2015 Set 1 (1) GATE ME 2015 Set 3 (1) GATE ME 2014 Set 1 (1) GATE ME 2013 (1) GATE ME 2009 (1) GATE ME 2008 (1) GATE ME 2007 (1)

GATE ME Subjects

Engineering Mechanics

Machine Design

Strength of Materials

Heat Transfer

Production Engineering

Industrial Engineering

Turbo Machinery

Theory of Machines

Engineering Mathematics

Fluid Mechanics

Thermodynamics

General Aptitude