PrepRung
Sign inSign up free

NDA 2020 Maths · Mathematics · Vector Algebra · easy

A vector of magnitude 14 in the direction of 2hat i+3hat j+6hat k is

Single correct option

A vector of magnitude 1414 in the direction of 2i^+3j^+6k^2\hat i+3\hat j+6\hat k is
  1. A. 2i^+3j^+6k^2\hat i+3\hat j+6\hat k
  2. B. 4i^+6j^+12k^4\hat i+6\hat j+12\hat k
  3. C. 14i^+21j^+42k^14\hat i+21\hat j+42\hat k
  4. D. i^+32j^+3k^\hat i+\dfrac32\hat j+3\hat k
Show answer and solution

Answer: (B) 4i^+6j^+12k^4\hat i+6\hat j+12\hat k

The magnitude of 2i^+3j^+6k^2\hat i+3\hat j+6\hat k is 4+9+36=7\sqrt{4+9+36}=7. A vector of magnitude 1414 in the same direction is 147(2i^+3j^+6k^)=4i^+6j^+12k^\dfrac{14}{7}(2\hat i+3\hat j+6\hat k)=4\hat i+6\hat j+12\hat k. The given vector itself has magnitude 77, the third option has magnitude 9898, which comes from multiplying by 1414 without dividing by 77, and the last option has magnitude 3.53.5, i.e. half of 77.
Report a mistake

Original question written in the NDA 2020 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake