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Find the point of intersection the plane 3x-y+2z-3=0 and the straight line (x+1)/3=(y+1)/2=(z-1)/-2
Find the radius of the sphere which passes through the points ( 0,0 ,0 ),(1,0,0 ),(0,1,0)
and (0,0,1)
and (0,0,1)
Given that
A
=
sin
t
i
+
cos
t
j
+
t
k
A=sinti+costj+tk
, evaluate
∣
∣
∣
d
2
A
d
t
2
∣
∣
∣
|d2Adt2|
A
=
sin
t
i
+
cos
t
j
+
t
k
A=sinti+costj+tk
, evaluate
∣
∣
∣
d
2
A
d
t
2
∣
∣
∣
|d2Adt2|
Determine the unit tangent at the point where t=2 on the curve
x
=
t
2
+
1
x=t2+1
,
y
=
4
t
−
3
y=4t−3
and
z
=
2
t
2
−
6
t
x
=
t
2
+
1
x=t2+1
,
y
=
4
t
−
3
y=4t−3
and
z
=
2
t
2
−
6
t
Determine the constant b such that
A
=
(
b
x
+
4
y
2
z
)
i
+
(
x
3
s
i
n
z
−
3
y
)
j
–
(
e
x
+
4
c
o
s
x
2
y
)
k
A=(bx+4y2z)i+(x3sinz−3y)j–(ex+4cosx2y)k
is a solenoidal
A
=
(
b
x
+
4
y
2
z
)
i
+
(
x
3
s
i
n
z
−
3
y
)
j
–
(
e
x
+
4
c
o
s
x
2
y
)
k
A=(bx+4y2z)i+(x3sinz−3y)j–(ex+4cosx2y)k
is a solenoidal
Find the unit outward drawn normal to the surface
(
x
−
1
)
2
+
y
2
+
(
z
+
2
)
2
(x−1)2+y2+(z+2)2
= 9 at the point (3, 1, -4)
(
x
−
1
)
2
+
y
2
+
(
z
+
2
)
2
(x−1)2+y2+(z+2)2
= 9 at the point (3, 1, -4)
If
f
=
x
2
y
z
f=x2yz
and
g
=
x
y
−
3
z
2
g=xy−3z2
, calculate $$ \triangledown\cdot (\triangledown f x \triangledown g)
f
=
x
2
y
z
f=x2yz
and
g
=
x
y
−
3
z
2
g=xy−3z2
, calculate $$ \triangledown\cdot (\triangledown f x \triangledown g)
Determine the constants a and b such that the curl of
(
2
x
y
+
3
y
z
)
i
+
(
x
2
+
a
x
z
–
4
z
2
)
j
+
(
3
x
y
+
2
b
y
z
)
k
=
0
(
2
x
y
+
3
y
z
)
i
+
(
x
2
+
a
x
z
–
4
z
2
)
j
+
(
3
x
y
+
2
b
y
z
)
k
=
0
A = Sin^-1 Root 3/2 + Sin^-1 1/3
B = Cos^-1 Root 3/2 + Cos^-1 1/3
Show That B > A
B = Cos^-1 Root 3/2 + Cos^-1 1/3
Show That B > A
Perform convolution for the signals x1(t) = 1; 1<t<10 and x2(t) = 1; 2<t<10
With
Objective
Concept/Theory
Method/Procedure
Manual calculations
Program
Output Graphs (Print outs)
Conclusion
Inference
With
Objective
Concept/Theory
Method/Procedure
Manual calculations
Program
Output Graphs (Print outs)
Conclusion
Inference
