Question

For any two vectors $\overrightarrow { \boldsymbol { A } }$ and $\vec { B }$ if $\overrightarrow { \boldsymbol { A } }$ .=|×|, the

magnitude of $\vec { A }$+ $\vec { B }$ is equal to

• A. $\sqrt { A ^ { 2 } + B ^ { 2 } }$
• B. A + B
• C. [A² + B² + $\left[ A ^ { 2 } + B ^ { 2 } + \frac { A B } { \sqrt { 2 } } \right] ^ { 1 / 2 }$
• D. (A² + B² + $\sqrt { 2 }$× AB)^1/2

Answer 1

Answer: (D)

(A² + B² + $\sqrt { 2 }$× AB)^1/2

Answer 2

. $\vec { B }$ =AB cosθ . . . (1)

|× $\vec { B }$ |= AB sinθ . . . (2)

∴ AB cosθ = AB sinθ ⇒ θ = 45⁰

Again given $\overrightarrow { \mathrm { C } }$ =+ $\vec { B }$

∴ | $\overrightarrow { \mathrm { C } }$ | = (A² + B² + 2ABcos45°)^1/2

= (A² + B² + √2AB)^1/2

Hence (4) is correct.