Q51 / 200 · AP EAMCET 2001 · Mathematics

If $\mathbf{a}=\hat{\mathbf{i}}+4 \hat{\mathbf{j}}, \mathbf{b}=2 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}, \mathbf{c}=5 \hat{\mathbf{i}}+9 \hat{\mathbf{j}}$, then $\mathbf{c}$ is equal to

  • A
    $2 \mathbf{a}+\mathbf{b}$
  • B
    $\mathbf{a}+2 \mathbf{b}$
  • Correct answer
    C
    $3 \mathbf{a}+\mathbf{b}$
  • D
    $\mathbf{a}+3 \mathbf{b}$

Solution

$\begin{aligned} 3 \mathbf{a}+\mathbf{b} & =3(\hat{\mathbf{i}}+4 \hat{\mathbf{j}})+2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}} \\ & =3 \hat{\mathbf{i}}+12 \hat{\mathbf{j}}+2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}=5 \hat{\mathbf{i}}+9 \hat{\mathbf{j}}=\mathbf{c}\end{aligned}$

Hence, the correct answer is option: 'C'.

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