1
GATE CE 2012
MCQ (Single Correct Answer)
+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 GATE CE 2012 Engineering Mathematics - Vector Calculus Question 1 English
A
$$ad-bc$$
B
$$ac+bd$$
C
$$ad+bc$$
D
$$ab-cd$$
2
GATE CE 2011
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
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Fluid Mechanics and Hydraulic Machines
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