Bài tập: Cho\( \overrightarrow{a} = (1, 1, 2), \, \overrightarrow{b} = (x, 0, 1)\).Tìm x để \(|\overrightarrow{a} + \overrightarrow{b}| = \sqrt{26}\)
A. \(\left[ \begin{array}{l} x = 2 \\ x = -4 \end{array} \right.\quad\)
B. \(\left[ \begin{array}{l} x = 2 \\ x = 4 \end{array} \right.\quad \)
C. \(\left[ \begin{array}{l} x = 3 \\ x = -5 \end{array} \right.\quad \)
D. \(\left[ \begin{array}{l} x = 2 \\ x = 3 \end{array} \right.\quad \)
Đáp án:
• \(\overrightarrow{a} + \overrightarrow{b} = (x+1, 1, 3)\)
• \(|\overrightarrow{a} + \overrightarrow{b}| = \sqrt{(x+1)^2 + 1 + 9} = \sqrt{26}\)
\( \Leftrightarrow (x+1)^2 = 16 \Leftrightarrow \left[ \begin{array}{l} x+1 = 4 \\ x+1 = -4 \end{array} \right. \Leftrightarrow \left[ \begin{array}{l} x = 3 \\ x = -5 \end{array} \right. \)
\(\Rightarrow\) Vậy chọn \(\boxed{\text{C}} \)