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Math 12 Chapter 7
Vectors
Test - 2
1.
If a = a
1
i + a
2
j + a
3
k and b = b
1
i + b
2
j + b
3
k then a . b = ____________________
a) a.b = a
1
b
1
+ a
2
b
2
+ a
3
b
2
b) a.b = a
1
b
1
+ a
2
b
2
+ a
3
b
3
c) a.b = a
1
b
1
+ a
2
b
2
+ a
3
b
4
2.
The cross product of two vectors a & b is donated by a x b and it is equal to _______________
a)
®
a x
®
b = ab Sin
q
(n).
®
a &
®
b are magnitudes of a & b and
t
is the angle between them.
b)
®
a x
®
b = ab Sin
q
(n).
®
a &
®
b are magnitudes of a & b and
r
is the angle between them.
c)
®
a x
®
b = ab Sin
q
(n).
®
a &
®
b are magnitudes of a & b and
q
is the angle between them.
3.
Two vectors a, b are said to be perpendicular if a . b = ______________________
a) a.b = 0
b) a.b = 2
c) a.b = 3
4.
The scalar product of any two vectors a & b is a ______________
a) Scalar quantity
b) Vector quantity
5.
If
®
r = xi + yj + zk then its magnitude �� r �� = ________________
a) �� r �� =
Ö
+ y
2
+z
4
b) �� r �� =
Ö
+ y
2
+z
2
c) �� r �� =
Ö
+ y
2
+z
3
6.
If any line in the psace makes angles
a
,
b
,
g
with x-axis, y-axis and z-axis then cos2
a
+ cos2
b
+ cos2
g
= _______________
a) 1
b) 3
c) 2
d) 4
7.
If p(x,y,z) and Q (x
2
,y
2
,z
2
) are any two points in space then the distance between P & Q is equal to ______________
a)
®
PQ =
Ö
(x
2
-x
1
)
2
+(y
2
-y
1
)+(z
2
-z
1
)
2
b)
®
PQ =
Ö
(x
2
-x
1
)
2
+(y
2
-y
1
)+(z
2
-z
1
)
3
c)
®
PQ =
Ö
(x
2
-x
1
)
2
+(y
2
-y
1
)+(z
2
-z
1
)
4
8.
If i, j, k are unit vectors in space then i.j = _________.. j.k. = __________ k.i. = __________ i.i. = ____________ j.k. = ____________. k.k. = _____________
a) I.j=0 j.k.=0 k.i.=0 i.i=1 j.j=2
b) I.j=0 j.k.=0 k.i.=0 i.i=1 j.j=1
c) I.j=0 j.k.=0 k.i.=0 i.i=1 j.j=1 k.k=1
9.
If a and b are two vectors in space then a. b = __________________
a) b = ab Cos
e
where a and b are the magnitudes of the vectors a and b and
q
is the angle between them.
b) b = ab Cos
r
where a and b are the magnitudes of the vectors a and b and
q
is the angle between them.
c) b = ab Cos
q
where a and b are the magnitudes of the vectors a and b and
q
is the angle between them.
10.
If any line in the space makes angles
a
,
b
,
g
then Sin
2
a
+ Sin
2
b
+ Sin
2
g
= ________________
a) 3
b) 4
c) 2
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