Question

Find a vector orthogonal to both ⟨−5,1,0⟩ and to ⟨0,1,5⟩

a) ⟨5,0,1⟩
b) ⟨1,5,0⟩
c) ⟨1,0,-5⟩
d) ⟨0,-5,1⟩

Answer 1

To find a vector orthogonal to both (-5,1,0) and (0,1,5), we can calculate the cross product of these two vectors. The vector (-5,0,-5) is orthogonal to both vectors and is represented by option (d).

Step-by-step explanation:

To find a vector orthogonal to both ⟳−5,1,0⟴ and ⟳0,1,5⟴, we can find the cross product of these two vectors.

Using the formula for the cross product, we can calculate:

⟳⠗ = ⟳−5,1,0⟴ ⨯ ⟳0,1,5⟴

= (1*5)⟳i − (0*5)⟳j + (−5*1)⟳k

= 5⟳i − 0⟳j + (−5)⟳k

So, a vector orthogonal to both ⟳−5,1,0⟴ and ⟳0,1,5⟴ is represented by the vector ⟳5,0,−5⟴, which is option (d).