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Byju's Answer
Standard XII
Mathematics
Theorems on Integration
lf P + Q = ...
Question
lf
→
P
+
→
Q
=
→
R
and
→
P
−
→
Q
=
→
S
, then
R
2
+
S
2
is equal to:
A
P
2
+
Q
2
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B
2
(
P
2
−
Q
2
)
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C
2
(
P
2
+
Q
2
)
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D
4
P
Q
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Solution
The correct option is
D
2
(
P
2
+
Q
2
)
R
2
=
P
2
+
Q
2
+
2
P
Q
c
o
s
A
S
2
=
P
2
+
Q
2
−
2
P
Q
c
o
s
A
where A is the angle between
→
P
and
→
Q
R
2
+
S
2
=
2
(
P
2
+
Q
2
)
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0
Similar questions
Q.
Let
p
,
q
a
n
d
r
be real numbers
(
p
≠
q
,
r
≠
0
)
, such that the roots of the equation
1
x
+
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+
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=
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are equal in magnitude but opposite in sign, then the sum of squares of these roots is equal to :
Q.
Find all triples
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=
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Q.
If p = −2, q = −1 and r = 3, find the value of
(i) p
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+ q
2
− r
2
(ii) 2p
2
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+ 3r
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(iii) p − q − r
(iv) p
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+ 3pqr
(v) 3p
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(vi) p
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Q.
If P : Q : R = 6 : 5 : 4 and
P
2
+
Q
2
+
R
2
=
192500
then find
(
P
+
Q
−
R
)
2
Q.
By how much must
2
p
2
q
2
−
3
p
2
q
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p
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