Question

If $| \mathbf { a } | + | \mathbf { b } | = | \mathbf { c } |$ and $\mathbf { a } + \mathbf { b } = \mathbf { c }$ then the angle between a and b is

• A. $\frac { \pi } { 2 }$
• B. $\pi$
• C. 0
• D. None of these

Answer 1

Answer: (C)

0

Answer 2

$\mathbf { a } + \mathbf { b } = \mathbf { c } \Rightarrow | \mathbf { a } | ^ { 2 } + | \mathbf { b } | ^ { 2 } + 2 \mathbf { a } \cdot \mathbf { b } = | \mathbf { c } | ^ { 2 }$

and $| \mathbf { a } | + | \mathbf { b } | = | \mathbf { c } |$ $\Rightarrow | \mathbf { a } | ^ { 2 } + | \mathbf { b } | ^ { 2 } + 2 | \mathbf { a } \| \mathbf { b } | = | \mathbf { c } | ^ { 2 }$

⇒ $\theta = 0$