AP EAMCET · Maths · Vector Algebra
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
- A \(x=1\)
- B \(x=-1\)
- C \(x=0\)
- D No such real \(x\) exist
Answer & Solution
Correct Answer
(A) \(x=1\)
Step-by-step Solution
Detailed explanation
\(|\mathbf{a}+\mathbf{b}|=|\mathbf{a}|+|\mathbf{b}| \Rightarrow \mathbf{a}, \mathbf{b}\) are in same direction. \[ \frac{1}{1}=\frac{x}{1}=\frac{1}{1} \Rightarrow x=1 \]
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