) Given two vectors, r1=3î + 2f – 3k and r2=2î + ĵ + k, show that both vectors lie inthe plane 5x – 9y – z = 0. (Note that the vector equation of a plane in the-summary sheets uses \mathbf{r}=x \hat{\imath}+y \hat{\jmath}+z \hat{k}) Find an equation of a plane that is perpendicular to the plane, 5x - 9y – z = 0,and in which the vector r2= 2î + ĵ + k lies. \text { Given the position vectors of three points } a=\hat{\imath}+\hat{\jmath}+\hat{k}, b=2 \hat{\imath}+3 \hat{\jmath}+\hat{k}, \mathbf{c}=3 \hat{\imath}+2 \hat{\jmath}+ 3k, find the equation of the plane passing through all three points.

Solved: ) Given two vectors, r1=3î + 2f – 3k and r2=2î + ĵ + k, show that bot

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given two vectors r13i 2f 3k and r22i j k show that both vectors lie i

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) Given two vectors, r1=3î + 2f – 3k and r2=2î + ĵ + k, show that both vectors lie inthe plane 5x – 9y – z = 0. (Note that the vector equation of a plane in the-summary sheets uses \mathbf{r}=x \hat{\imath}+y \hat{\jmath}+z \hat{k}) Find an equation of a plane that is perpendicular to the plane, 5x - 9y – z = 0,and in