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Byju's Answer
Standard XII
Mathematics
Chain Rule of Differentiation
If c #160; ...
Question
If
c
→
is perpendicular to both
a
→
and
b
→
, then prove that it is perpendicular to both
a
→
+
b
→
and
a
→
-
b
→
.
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Solution
Given that
c
→
is perpendicular to both
a
→
and
b
→
.
⇒
c
→
.
a
→
=
0
and
c
→
.
b
→
=
0
.
.
.
1
Now,
c
→
.
a
→
+
b
→
=
c
→
.
a
→
+
c
→
.
b
→
=
0
+
0
=
0
From
1
So,
c
→
is perpendicular to
a
→
+
b
→
.
Again
,
c
→
.
a
→
-
b
→
=
c
→
.
a
→
-
c
→
.
b
→
=
0
-
0
=
0
From
1
So,
c
→
is perpendicular to
a
→
-
b
→
.
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0
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