Which of the following is the unit vector perpendicular to vecA and vecB ?

Question

Which of the following is the unit vector perpendicular to vecA and vecB ? (A) ( hatA × hatB/A B sin θ) (B) ( hatA × hatB/A B cos θ) (C) ( vecA × vecB/A B sin θ) (D) ( vecA × vecB/A B cos θ)

Tardigrade Admin · Accepted Answer

Vector perpendicular to A and B, vecA × vecB=A B sin θ hatn ∴ Unit vector perpendicular to A and B hatn=( vecA × vecB/| vecA| ×| vecB| sin θ)

Q. Which of the following is the unit vector perpendicular to $A$ and $B$ ?

$\frac{A ^ \times B ^}{A B s i n θ}$

$\frac{A ^ \times B ^}{A B c o s θ}$

$\frac{A \times B}{A B s i n θ}$

$\frac{A \times B}{A B c o s θ}$

Vector perpendicular to $A$ and $B, A \times B = A B sin θ \overset{n}{^}$
$∴$ Unit vector perpendicular to $A$ and $B$
$\overset{n}{^} = \frac{A \times B}{∣ A ∣ \times ∣ B ∣ s i n θ}$

Q. Which of the following is the unit vector perpendicular to A and B ?

ABsinθA^×B^​

ABcosθA^×B^​

ABsinθA×B​

ABcosθA×B​