(1) Show that the vectors 2T + 27 + + 27 + 2K and 2T +1 -
2k are mutually orthogonal.
(Or)
( What is the unit yector
b)
nornandi
Answers
Answer:
Coefficient of x⁶y³ is 672.
Step-by-step explanation:
General term of expansion (a+b)ⁿ is
\bf \: T_{r+1} = \: \: ^nC_r \: \: \large \frak{ a ^{n−r} b ^r}T
r+1
=
n
C
r
a
n−r
b
r
For (x+2y)⁹,
Putting n =9, a=x, b=2y
\begin{gathered} \bf \: T_{r+1} = \: \: ^{9} C_r (x) ^{9−r} (2y) ^r \\ \\ \bf \: T _{r+1} = \: \: ^{9} C_r (x) ^{9−r} .(y) ^r .(2) ^r\end{gathered}
T
r+1
=
9
C
r
(x)
9−r
(2y)
r
T
r+1
=
9
C
r
(x)
9−r
.(y)
r
.(2)
r
Comparing with x⁶ y³ , we get, r = 3
Therefore,
\begin{gathered} \bf \: T _{r+1} \\ \: \tt ^9C_3 (x)^9−3 .y³ .2³ \\ \tt\: \: 9! (2)³× x⁶ × y³) / (3!.6!) \\ \: \tt 672x⁶ y³\end{gathered}
T
r+1
9
C
3
(x)
9
−3.y³.2³
9!(2)³×x⁶×y³)/(3!.6!)
672x⁶y³
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Answer:
Dimensions of Density are ML‐³
1 kg=1000 g,1 m=100 cm
Thus, 13.6 g/cc=13.6×(1000‐¹)×(100‐¹)‐³
=13.6×10 -3 ×10⁶
= 13.6×10³kg/m³