13

VECTOR
ALGEBRA
Page
2
( Answers
at
the
end
of
all
questions )
( 7 )
A
particle
is
acted
upon
by
constant
forces
^
^
^
k
3
j
i
4

+
and
^
^
^
k
j
i
3

+
which
displace
it
from
a
point
^
^
^
k
3
j
2
i
+
+
to
the
point
^
^
^
k
j
4
i
5
+
+
.
The
work
done
in
standard
units
by
the
forces
is
given
by
( a )
40
( b )
30
( c )
25
( d )
15
[ AIEEE
2004 ]
( 8 )
If
c
,
b
,
a
are
noncoplanar
vectors
and
λ
is
a
real
number,
then
the
vectors
c
3
b
2
a
+
+
,
c
4
b
+
λ
and
( 2
λ

1 )
c
are
noncoplanar
for
( a )
all
values
of
λ
( b )
all
except
one
value
of
λ
( c )
all
except
two
values
of
λ
( d )
no
value
of
λ
[ AIEEE
2004 ]
( 9 )
Let
w
,
v
,
u
be
such
that
l
u l
=
1,
l
v l
=
2
and
l
w l
=
3.
If
the
projection
of
v
along
u
is
equal
to
that
of
w
along
and
v ,
are
perpendicular
to
each
other,
then
l

+
equals
( a )
2
( b )
7
( c )
14
( d )
14
[ AIEEE
2004 ]
( 10 )
Let
c
,
b
,
a
be
nonzero
vectors
such
that
(
c
)
b
a
×
×
=
a
l
c
l
l
b
l
3
1
.
If
θ
is
the
acute
angle
between
the
vectors
c
and
b
,
then
sin
θ
equals
( a )
3
1
( b )
3
2
( c )
3
2
( d )
3
2
2
[ AIEEE
2004 ]
( 11 )
If
2
2
2
2
2
2
c
1
c
c
b
1
b
b
a
1
a
a
+
+
+
=
0
and
vectors
( 1,
a,
a
2
),
( 1,
b,
b
2
)
and
( 1,
c,
c
2
)
are
noncoplanar,
then
the
product
abc
equals
( a )
2
( b )
 1
( c )
1
( d )
0
[ AIEEE
2003 ]
( 12 )
→
→
→
c
,
b
,
a
are
three
vectors,
such
that
→
→
→
+
+
c
b
a
=
0,
l
→
a
l
=
1,
l
→
b
l
=
2,
l
→
c
l
=
3,
then
→
→
⋅
b
a
+
→
→
⋅
c
b
+
→
→
⋅
a
c
is
equal
to
( a )
0
( b )
 7
( c )
7
( d )
1
[ AIEEE
2003 ]