For any two vectors A and B, if A⋅ B =|A × B | , the magnitude of C = A + B is equal to

Question

For any two vectors A and B, if A⋅ B =|A × B | , the magnitude of C = A + B is equal to (A) √A2 + B2 (B) A + B (C) √A2 + B2 + (AB/√2) (D) √A2 + B2 + √2 AB

Tardigrade Admin · Accepted Answer

AB cos θ = AB sin θ ⇒ tan θ = 1 ⇒ θ = 45° ∴ |C| = √A2 + B2 + 2 AB cos 45° = √A2 + B2 + √2 AB

Q. For any two vectors A and B, if $A \cdot B = ∣ A \times B ∣$ , the magnitude of C = A + B is equal to

$A^{2} + B^{2}$

$A + B$

$A^{2} + B^{2} + \frac{A B}{2}$

$A^{2} + B^{2} + 2 A B$

$A B cos θ = A B sin θ \Rightarrow t an θ = 1 \Rightarrow θ = 4 5^{\circ}$
$∴ ∣ C ∣ = A^{2} + B^{2} + 2 A B cos 4 5^{\circ}$
$= A^{2} + B^{2} + 2 A B$

Q. For any two vectors A and B, if A⋅B=∣A×B∣ , the magnitude of C = A + B is equal to

A2+B2​

A+B

A2+B2+2​AB​​

A2+B2+2​AB​