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  • The position vector of a point P is <img alt="\overrightarrow{\mathbf{r}}=x \hat{\mathbf{i}}+y \hat{\mathbf{j}}+z \hat{\mathbf{k}}, \text{when } x, y, z \in N" src="https://entrancecorner.onco

The position vector of a point P is \overrightarrow{\mathbf{r}}=x \hat{\mathbf{i}}+y \hat{\mathbf{j}}+z \hat{\mathbf{k}}, \text{when } x, y, z \in N and \overrightarrow{\mathbf{a}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}. \text{If } \overrightarrow{\mathbf{r}} \cdot \overrightarrow{\mathbf{a}}=10, the number of possible position of P is

 

Option: 1

36


Option: 2

72


Option: 3

66


Option: 4

{ }^9 C_2


Answers (1)

best_answer

\begin{aligned} & \because \overrightarrow{\mathbf{r}} \cdot \overrightarrow{\mathbf{a}}=10 \\ & \therefore \quad x+y+z=10 ; x \geq 1, y \geq 1, z \geq 1 \end{aligned}

The required number of positions 

={ }^{10-1} C_{3-1}={ }^9 C_2=36

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Pankaj

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