For any vector a=a₁ i+a₂ j+a₃ k, with 10|a i |<1, i=1,2,3, consider the following statements: (A): max \|a₁|,|a₂|,|a₃| ≤|a| (B): |a| ≤ 3 max \|a₁|,|a₂|,|a₃|

(C) Neither (A) nor (B) is true

Vector Algebra: JEE Main 2023 Mathematics question

JEE Main 2023 · 11 Apr, Morning shift · Q5699

JEE Main 202311 Apr, Morning shiftMathematicsMediumVector Algebra184× since 2002

For any vector

\vec{a}=a_{1} \hat{i}+a_{2} \hat{j}+a_{3} \hat{k}

, with

10\left|a_{i}\right|<1, i=1,2,3

, consider the following statements : (A):

\max \left\{\left|a_{1}\right|,\left|a_{2}\right|,\left|a_{3}\right|\right\} \leq|\vec{a}|

(B) :

|\vec{a}| \leq 3 \max \left\{\left|a_{1}\right|,\left|a_{2}\right|,\left|a_{3}\right|\right\}