1
GATE CE 2012
+1
-0.3
For the parallelogram $$OPQR$$ shown in the sketch. $$\,\overrightarrow {OP} = a\widehat i + b\widehat j$$ and $$\,\overrightarrow {OR} = c\widehat i + d\widehat j.\,\,$$ The area of the parallelogram is
A
$$ad-bc$$
B
$$ac+bd$$
C
$$ad+bc$$
D
$$ab-cd$$
2
GATE CE 2011
+1
-0.3
If $$\overrightarrow a$$ and $$\overrightarrow b$$ are two arbitrary vectors with magnitudes $$a$$ and $$b$$ respectively, $${\left| {\overrightarrow a \times \overrightarrow b } \right|^2}$$ will be equal to
A
$${a^2}\,{b^2} - {\left( {\overrightarrow a .\,\overrightarrow b } \right)^2}$$
B
$$ab - \overrightarrow a .\,\overrightarrow b$$
C
$${a^2}\,{b^2} + {\left( {\overrightarrow a .\,\overrightarrow b } \right)^2}$$
D
$$ab + \overrightarrow a .\,\overrightarrow b$$
3
GATE CE 2009
+1
-0.3
For a scalar function $$f(x,y,z)=$$ $${x^2} + 3{y^2} + 2{z^2},\,\,$$ the gradient at the point $$P(1,2,-1)$$ is
A
$$2\widehat i + 6\widehat j + 4\widehat k$$
B
$$2\widehat i + 12\widehat j - 4\widehat k$$
C
$$2\widehat i + 12\widehat j + 4\widehat k$$
D
$$\sqrt {56}$$
4
GATE CE 2003
+1
-0.3
The vector field $$\,F = x\widehat i - y\widehat j\,\,$$ (where $$\widehat i$$ and $$\widehat j$$ are unit vectors) is
A
divergence free, but not irrotational
B
irrotational, but not divergence free
C
divergence free and irrotational
D
neither divergence free nor irrotational
GATE CE Subjects
Engineering Mechanics
Construction Material and Management
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
Geomatics Engineering Or Surveying
Environmental Engineering
Transportation Engineering
General Aptitude
EXAM MAP
Medical
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