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 4 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
$$ab + \overrightarrow a .\,\overrightarrow b $$
GATE CE Subjects
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12