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NDA Math Vector Algebra
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© examsnet.com
Question : 25
Total: 101
Two adjacent sides of a parallelogram are
2
^
i
−
4
^
j
+
5
^
k
and
^
i
−
2
^
j
−
3
^
k
. What is the magnitude of dot product of vectors which represent its diagonals?
[NDA-I 2020]
21
25
31
36
Validate
Solution:
👈: Video Solution
Let
→
a
=
2
∧
i
−
4
∧
j
+
5
∧
k
and
→
b
=
∧
i
−
2
∧
j
−
3
∧
k
Two diagonals of the parallelograms are given by
(
→
a
+
→
b
)
=
(
2
+
1
)
∧
i
−
(
4
+
2
)
∧
j
+
(
5
−
3
)
∧
k
=
3
∧
i
−
6
∧
j
+
2
∧
k
and
(
→
a
−
→
b
)
=
(
2
−
1
)
∧
i
−
(
4
−
2
)
∧
j
+
(
5
−
(
−
3
)
)
∧
k
=
∧
i
−
2
∧
j
+
8
∧
k
Dot products of the diagonals
(
→
a
+
→
b
)
⋅
(
→
a
−
→
b
)
=
(
3
∧
i
−
6
∧
j
+
2
∧
k
)
⋅
(
∧
i
−
2
∧
j
+
8
∧
k
)
=
(
3
+
12
+
16
)
=
31
units
© examsnet.com
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