2
You visited us
2
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Bijective Function
Using propert...
Question
Using properties of scalar triple product, prove that
[
¯
¯
¯
a
+
¯
¯
b
¯
¯
b
+
¯
¯
c
¯
¯
c
+
¯
¯
¯
a
]
=
2
[
¯
¯
¯
a
¯
¯
b
¯
¯
c
]
.
Open in App
Solution
We have to prove that
[
¯
¯
¯
a
+
¯
¯
b
¯
¯
b
+
¯
¯
c
¯
¯
c
+
¯
¯
¯
a
]
=
2
[
¯
¯
¯
a
¯
¯
b
¯
¯
c
]
(
¯
¯
¯
a
+
¯
¯
b
)
.
(
(
¯
¯
b
+
¯
¯
c
)
(
¯
¯
c
+
¯
¯
¯
a
)
)
(
¯
¯
¯
a
+
¯
¯
b
)
.
(
¯
¯
b
×
¯
¯
c
+
¯
¯
b
×
¯
¯
¯
a
+
¯
¯
c
×
¯
¯
¯
a
)
[
¯
¯
¯
a
¯
¯
b
¯
¯
c
]
+
[
¯
¯
¯
a
¯
¯
b
¯
¯
c
]
=
2
[
¯
¯
¯
a
¯
¯
b
¯
¯
c
]
Hence, proved.
Suggest Corrections
0
Similar questions
Q.
Using property of scalar triple product, prove that
(
¯
a
+
¯
b
+
¯
c
)
×
(
¯
b
−
¯
a
)
⋅
¯
c
=
2
¯
a
⋅
¯
b
×
¯
c
.
Q.
Using properties of determinants, prove the following:
∣
∣ ∣
∣
a
b
c
a
−
b
b
−
c
c
−
a
b
+
c
c
+
a
a
+
b
∣
∣ ∣
∣
=
a
3
+
b
3
+
c
3
−
3
a
b
c
Q.
Using properties of determinants, prove the following :
⎡
⎢
⎣
a
a
2
b
c
b
b
2
c
a
c
c
2
a
b
⎤
⎥
⎦
=
(
a
−
b
)
(
b
−
c
)
(
c
−
a
)
(
b
c
+
c
a
+
a
b
)
Q.
Using the properties of determinant and without expanding , prove that:
∣
∣ ∣
∣
a
−
b
b
−
c
c
−
a
b
−
c
c
−
a
a
−
b
c
−
a
a
−
b
b
−
c
∣
∣ ∣
∣
=
0
Q.
By using properties of determinants, show that:
(i)
(ii)