Question

(1 point) Find two unit vectors orthogonal to a=⟨4,5,0⟩a=⟨4,5,0⟩ and b=⟨0,1,−3⟩b=⟨0,1,−3⟩ Enter your answer so that the first non-zero coordinate of the first vector is positive. First Vector: ⟨⟨ , , ⟩⟩ Second Vector: ⟨⟨ , , ⟩

Answer 1

Answer:

 First vector

$V=+ \dfrac{-15i+12j+4k}{\sqrt{385}}$

Second vector

$V=- \dfrac{-15i+12j+4k}{\sqrt{385}}$

Step-by-step explanation:

Given that

Vector a ,  a= 4 i + 5 j + 0 k

Vector b , b= 0 i + 1 j  - 3 k

The orthogonal vector V is given as

V = a x b

V is the cross product of the above two vector which is orthogonal to the vectors a and b.

$V=\begin{vmatrix}i & j & k\\ 4 & 5 & 0\\ 0& 1 &-3 \end{vmatrix}\\V=i(-15-0)-j(-12-0)+k(4-0)\\V=-15i+12j+4k$

The unit vectors

$V=\pm \dfrac{-15i+12j+4k}{\sqrt{15^2+12^2+4^2}}\\\\V=+\dfrac{-15i+12j+4k}{\sqrt{385}}\\V=-\dfrac{-15i+12j+4k}{\sqrt{385}}$

First vector

$V=+ \dfrac{-15i+12j+4k}{\sqrt{385}}$

Second vector

$V=- \dfrac{-15i+12j+4k}{\sqrt{385}}$