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MHTCET 2016 Math Solved Paper
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© examsnet.com
Question : 29
Total: 50
If a =
→
a
=
^
i
+
^
j
−
2
^
k
,
→
b
=
2
^
i
−
^
j
+
^
k
and
→
c
=
3
^
i
−
^
k
and
→
c
=
m
→
a
+
n
→
b
, then m + n is equal to
0
1
2
-1
Validate
Solution:
(c) Given,
→
a
=
^
i
+
^
j
−
2
^
k
,
→
b
=
2
^
i
−
^
j
+
^
k
,
→
c
=
3
^
i
−
^
k
and
→
c
=
m
→
a
+
n
→
b
As,
3
^
i
−
^
k
=
m
(
^
i
+
^
j
−
2
^
k
)
+
n
(
2
^
i
−
^
j
+
^
k
)
⇒
3
^
i
−
^
k
=
(
m
+
2
n
)
^
i
+
(
m
−
n
)
^
j
+
(
−
2
m
+
n
)
^
k
After equating the coefficient of
^
i
,
^
j
and
^
k
, on both sides respectively, we get
3 = m + 2n, 0 = m - n and -1 = - 2 m + n
⇒ 3 = n + 2n ⇒ n = 1
⇒ m = 1 and n = 1
⇒ m + n = 1+ 1 = 2
© examsnet.com
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