1
GATE PI 2012
+1
-0.3
For the spherical surface $${x^2} + {y^2} + {z^2} = 1,$$ the unit outward normal vector at the point $$\left( {{1 \over {\sqrt 2 }},{1 \over {\sqrt 2 }},0} \right)$$ is given by
A
$${{1 \over {\sqrt 2 }}\widehat i + {1 \over {\sqrt 2 }}\widehat j}$$
B
$${{1 \over {\sqrt 2 }}\widehat i - {1 \over {\sqrt 2 }}\widehat j}$$
C
$${\widehat k}$$
D
$${{1 \over {\sqrt 3 }}\widehat i + {1 \over {\sqrt 3 }}\widehat j + {1 \over {\sqrt 3 }}\widehat k}$$
2
GATE PI 2011
+1
-0.3
If $$A$$ $$(0,4,3),$$ $$B(0,0,0)$$ and $$C(3,0,4)$$ are there points defined in $$x, y, z$$ coordinate system, then which one of the following vectors is perpendicular to both the vectors $$\overrightarrow {AB}$$ and $$\overrightarrow {BC}$$.
A
$$16\widehat i + 9\widehat j - 12\widehat k$$
B
$$16\widehat i - 9\widehat j + 12\widehat k$$
C
$$16\widehat i - 9\widehat j - 12\widehat k$$
D
$$16\widehat i + 9\widehat j + 12\widehat k$$
3
GATE PI 2009
+1
-0.3
The line integral of the vector function $$\overrightarrow F = 2x\widehat i + {x^2}\widehat j\,\,$$ along the $$x$$ - axis from $$x=1$$ to $$x=2$$ is
A
$$0$$
B
$$2.33$$
C
$$3$$
D
$$5.33$$
4
GATE PI 2008
+1
-0.3
If $$\overrightarrow r$$ is the position vector of any point on a closed surface $$S$$ that encloses the volume $$V$$ then $$\,\,\int {\int\limits_s {\left( {\overrightarrow r \,.\,d\overrightarrow s } \right)\,\,} }$$ is equal to
A
$${1 \over 2}V$$
B
$$V$$
C
$$2V$$
D
$$3V$$
GATE PI Subjects
Engineering Mechanics
Theory of Machines
Machine Design
Fluid Mechanics
Thermodynamics
Casting
Joining of Materials
Metal Forming
Machine Tools and Machining
Metrology
Industrial Engineering
EXAM MAP
Medical
NEET