Q69 / 160 · AP EAMCET 2022 (07 Jul Shift 2) · Mathematics

Let $\mathbf{a}=\hat{i}+x \hat{j}+\hat{k}, \mathbf{b}=\hat{i}+\hat{j}+\hat{k}$ and $|\mathbf{a}+\mathbf{b}|=|\mathbf{a}|+|\mathbf{b}|$, then

  • Correct answer
    A
    $x=1$
  • B
    $x=-1$
  • C
    $x=0$
  • D
    No such real $x$ exist

Solution

$|\mathbf{a}+\mathbf{b}|=|\mathbf{a}|+|\mathbf{b}| \Rightarrow \mathbf{a}, \mathbf{b}$ are in same direction. $$ \frac{1}{1}=\frac{x}{1}=\frac{1}{1} \Rightarrow x=1 $$

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

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