+0

# The vector $\begin{pmatrix} 4 \\ -7 \end{pmatrix}$ is orthogonal to the vector $\begin{pmatrix} 3 \\ k \end{pmatrix}$. The vector \$\begin{pm

0
52
1

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
+96080
+1

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

Feb 2, 2019