Question

Which of the following vector is/are equal to vector AB, where A(0,0) and B(1,1).

• A.
  CD where C(0,0) and D(-1,-1)
• B.
  EF where E(-1,0) and F(0,1)
• C.
  GH where G(0,0) and H(2,2)
• D.
  IJ where I(0,0) and J(0,1)

Answer 1

The correct option is B

EF where E(-1,0) and F(0,1)
$\overrightarrow{AB}=\overrightarrow{OB}-\overrightarrow{OA}=(1-0)i+(1-0)j=i+j$
Similarly for other vectors

$\overrightarrow{CD}=\overrightarrow{OD}-\overrightarrow{OC}=(-1-0)i+(-1-0)j=-(i+j)$
$\overrightarrow{EF}=\overrightarrow{OE}-\overrightarrow{OF}=(0-(-1\left)\right)i+(1-0)j=i+j$
$\overrightarrow{GH}=\overrightarrow{OH}-\overrightarrow{OG}=(2-0)i+(2-0)j=2(i+j)$
$\overrightarrow{IJ}=\overrightarrow{OJ}-\overrightarrow{OI}=(0-0)i+(1-0)j=j$
It is clearly seen that vector EF is equal to vector AB.