Question

The position vector of a point P is –

$\overset{\rightarrow}{r}$ = x $\overset{\rightarrow}{i}$+ y$\overset{\rightarrow}{j}$ + z $\overset{\rightarrow}{k}$, where x Ī N, yĪ N, z Ī N and

$\overset{\rightarrow}{a}$ = $\overset{\rightarrow}{i}$ + $\overset{\rightarrow}{j}$ + $\overset{\rightarrow}{k}$. If $\overset{\rightarrow}{r}$ . $\overset{\rightarrow}{a}$ = 10, the number of possible position of P is –]

• A. 36
• B. 72
• C. 66
• D. None of these

Answer 1

Answer: (A)

36

Answer 2

$\overset{\rightarrow}{r}$.$\overset{\rightarrow}{a}$ = 10 Ž x + y + z = 10 ,x, y, z Ī N : - no. of Integral point = ^{10 –1}C_3–1 = ⁹C₂ = 36