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Question: If **a** has magnitude 5 and points north-east and vector **b** has magnitude 5 and points north-wes...

If a has magnitude 5 and points north-east and vector b has magnitude 5 and points north-west, then ∣a−b∣=| \mathbf { a } - \mathbf { b } | =

A

25

B

5

C

737 \sqrt { 3 }

D

525 \sqrt { 2 }

Answer

525 \sqrt { 2 }

Explanation

Solution

Since a⊥b⇒a⋅b=0\mathbf { a } \perp \mathbf { b } \Rightarrow \mathbf { a } \cdot \mathbf { b } = 0

∣a−b∣2=(a−b)2=a2+b2−2a⋅b=25+25| \mathbf { a } - \mathbf { b } | ^ { 2 } = ( \mathbf { a } - \mathbf { b } ) ^ { 2 } = a ^ { 2 } + b ^ { 2 } - 2 \mathbf { a } \cdot \mathbf { b } = 25 + 25

⇒∣a−b∣=52\Rightarrow | \mathbf { a } - \mathbf { b } | = 5 \sqrt { 2 }