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Byju's Answer
Standard XII
Mathematics
Orthogonal System of Vectors
If a →= i ∧+2...
Question
If
a
→
=
i
^
+
2
j
^
-
3
k
^
and
b
→
=
2
i
^
+
4
j
^
+
9
k
^
,
find a unit vector parallel to
a
→
+
b
→
.
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Solution
Given:
a
→
=
i
^
+
2
j
^
-
3
k
^
,
b
→
=
2
i
^
+
4
j
^
+
9
k
^
Now
,
a
→
+
b
→
=
3
i
^
+
6
j
^
+
6
k
^
a
→
+
b
→
=
3
2
+
6
2
+
6
2
=
9
+
36
+
36
=
81
=
9
Unit vector parallel to
a
→
+
b
→
=
a
→
+
b
→
a
→
+
b
→
=
3
i
^
+
6
j
^
+
6
k
^
9
=
1
9
×
3
i
^
+
2
j
^
+
2
k
^
=
1
3
i
^
+
2
j
^
+
2
k
^
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0
Similar questions
Q.
Find the cross products of the vectors
1.
a
=
i
−
2
j
+
3
k
,
b
=
3
i
−
6
j
+
9
k
2.
a
=
−
2
i
−
4
k
,
b
=
i
−
2
j
−
k
,
c
=
i
−
4
j
+
3
k
Q.
The two adjacent sides of a parallelogram,
→
a
=
2
i
+
4
j
−
5
k
and
→
b
=
i
+
2
j
+
3
k
, then find the unit vector parallel to its diagonal.
Q.
The sides of a parallelogram are
2
i
+
4
j
−
5
k
and
i
+
2
j
+
3
k
.
Find the unit vectors parallel to the diagonals.
Q.
If
a
→
=
i
^
+
j
^
+
k
^
,
b
→
=
2
i
^
-
j
^
+
3
k
^
and
c
→
=
i
^
-
2
j
^
+
k
^
,
find a unit vector parallel to
2
a
→
-
b
→
+
3
c
.
→
Q.
The unit vector in the direction of sum of the vectors
→
A
=
2
ˆ
i
+
4
ˆ
j
−
7
ˆ
k
and
→
B
=
4
ˆ
i
−
6
ˆ
j
+
4
ˆ
k
will be
