Answer:
Explanation:
You can use the cross product. Let the vector that perpendicular to a and c is [tex]\vec{d}[/tex], so:
[tex]\vec{d}=\vec{a}\times\vec{c}=\left|\left[\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\5&4&-6\\4&3&2\end{array}\right] \right|=(8+18)\hat{i}-\hat{j}(10+24)+\hat{k}(15-16)=26\hat{i}-34\hat{j}-\hat{k}[/tex]
To check that c is perpendicular with a and b, do the dot product between c and a and also c and b and if the result is zero, you're true.
[tex]\vec{d}.\vec{a}=(26*5)-(34*4)+(6)=0[/tex] (c perpendicular to a)
[tex]\vec{d}.\vec{c}=(4*26)-(34*3)-(2*1)=0[/tex] (d perpendicular to c)
