Let a be real number and x = i +2 j , =2 i +a j +10 k , y =12 i +20 j +a k be three…
Mathematics · JEE Main · NTA Exams — Vector Algebra
Let a be real number and \(\vec{x}=\hat{i}+2 \hat{j}, \cdot \vec{\beta}=2 \hat{i}+a \hat{j}+10 \hat{k}, \vec{y}=12 \hat{i}+20 \hat{j}+a \hat{k}\) be three vectors, then \(\vec{x}, \vec{\beta} \text { and } \vec{y}\) are :
- Linearly dependent for all a
- Linearly independent for all a
- Linearly dependent for a < 0
- Linearly dependent for a > 0
Answer
(A) Linearly dependent for all a
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