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The vector \(\begin{pmatrix} 4 \\ -7 \end{pmatrix}\) is orthogonal to the vector \(\begin{pmatrix} 3 \\ k \end{pmatrix}\). The vector \(\begin{pmatrix} 2 \\ m \end{pmatrix}\) is orthogonal to the vector \(\begin{pmatrix} 3 \\ k \end{pmatrix}\). Find m .

 Feb 2, 2019
 #1
avatar+99523 
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If vectors are orthagonal, their dot product = 0

 

So

 

[ 4 * 3 ] + [ -7 * k] = 0

12 - 7k = 0

-7k = -12

k = 12/7

 

So

[2 * 3 ] + [12/7 * m] = 0

6 + (12/7)m = 0

(12/7)m = - 6

m = -6*7/12 = -7/2

 

 

cool cool cool

 Feb 2, 2019

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