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anonymous
 5 years ago
Find all the vectors n= (a,b,c) which are perpendicular to both vectors r1 and r2.
r1=(3,7,8)
r2=(1,8,1)
anonymous
 5 years ago
Find all the vectors n= (a,b,c) which are perpendicular to both vectors r1 and r2. r1=(3,7,8) r2=(1,8,1)

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You can find these vectors by taking the cross product of r1 and r2. Solution: The cross product of r1 and r2 is \[r_1\times r_2=\left\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\3&7&8\\1&8&1\end{array}\right=(764)\hat{i}(38)\hat{j}+(247)\hat{k}=\] \[57\hat{i}+5\hat{j}+17\hat{k}=(57;5;17).\] So the vectors that are perp. to r1 and r2: \[\{(57t;5t;17t;)\mid t\in\mathbb{R}\}.\]
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