Q 15. Find the value of n so that vector 21 - 3ị + k may be perpendicular to the vector 31 - 4j + nk. by-6 c)18 d)-18 a) 6
Answers
Answered by
1
Answer:
Given,
a
=3
i
^
+2
j
^
+2
k
^
and
b
=
i
^
+2
j
^
−2
k
^
.
Now,
a
+
b
=(3
i
^
+2
j
^
+2
k
^
)+(
i
^
+2
j
^
−2
k
^
)=4
i
^
+4
j
^
+0
k
^
a
−
b
=(3
i
^
+2
j
^
+2
k
^
)−(
i
^
+2
j
^
−2
k
^
)=2
i
^
+0
j
^
+4
k
^
We know that the unit vector perpendicular to both
a
+
b
ane
a
−
b
is given by
n
^
=
∣
∣
∣
∣
(
a
+
b
)×(
a
−
b
)
∣
∣
∣
∣
(
a
+
b
)×(
a
−
b
)
Here, (
a
+
b
)×(
a
−
b
)=
∣
∣
∣
∣
∣
∣
∣
∣
i
^
4
2
j
^
4
0
k
^
0
4
∣
∣
∣
∣
∣
∣
∣
∣
=
i
^
(16−0)−
j
^
(16−0)+
k
^
(0−8)
=16
i
^
−16
j
^
−8
k
^
Now,
∣
∣
∣
∣
(
a
+
b
)×(
a
−
b
)
∣
∣
∣
∣
=
(16)
2
+(16)
2
+(8)
2
=
256+256+64
=
576
=24
Hence, the required unit vector
n
^
=
∣
∣
∣
∣
(
a
+
b
)×(
a
−
b
)
∣
∣
∣
∣
(
a
+
b
)×(
a
−
b
)
=
24
16
i
^
−16
j
^
−8
k
^
=
3
2
i
^
−
3
2
j
^
−
3
1
k
^
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