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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Vector Algebra

NDA 2012 · Mathematics · Vector Algebra

ABCD is a parallelogram. If AB = a , BC = b , then what is BD equal...

ABCD is a parallelogram. If AB→=a⃗,BC→=b⃗\overrightarrow{\mathrm{AB}}=\vec{a}, \overrightarrow{\mathrm{BC}}=\vec{b}, then what is BD→\overrightarrow{\mathrm{BD}} equal to?

Options

  1. Aa⃗+b⃗\vec{a}+\vec{b}
  2. Ba⃗−b⃗\vec{a}-\vec{b}
  3. C−a⃗−b⃗-\vec{a}-\vec{b}
  4. D−a⃗+b⃗-\vec{a}+\vec{b}

Correct answer

D. −a⃗+b⃗-\vec{a}+\vec{b}

Step-by-step solution

BC→=AD→AB→+BD→=AD→∴BD→=AD→−AB→⇒bˉ−aˉ\overrightarrow{\mathrm{BC}}=\overrightarrow{\mathrm{AD}}\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{BD}}=\overrightarrow{\mathrm{AD}}\therefore \quad \overrightarrow{\mathrm{BD}}=\overrightarrow{\mathrm{AD}}-\overrightarrow{\mathrm{AB}}\Rightarrow \quad \bar{b}-\bar{a}.
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