1
GATE CE 2023 Set 2
MCQ (Single Correct Answer)
+1
-0.33
Let πœ™ be a scalar field, and 𝒖 be a vector field. Which of the following identities is true for div(πœ™π’–)?
A
div(πœ™π’–) = πœ™div(𝒖) + 𝒖 β‹… grad(πœ™)
B
div(πœ™π’–) = πœ™div(𝒖) + 𝒖 Γ— grad(πœ™)
C
div(πœ™π’–) = πœ™grad(𝒖) + 𝒖 β‹… grad(πœ™)
D
div(πœ™π’–) = πœ™grad(𝒖) + 𝒖 Γ— grad(πœ™)
2
GATE CE 2017 Set 2
Numerical
+1
-0
The divergence of the vector field $$\,V = {x^2}i + 2{y^3}j + {z^4}k\,\,$$ at $$x=1, y=2, z=3$$ is ________.
Your input ____
3
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 5 English
A
$$ad-bc$$
B
$$ac+bd$$
C
$$ad+bc$$
D
$$ab-cd$$
4
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
$$ab + \overrightarrow a .\,\overrightarrow b $$
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