By signing in you confirm you are 18 or older, or have your parent’s or guardian’s consent.

NDA 2 2024 Maths, question 55

Topic: Vectors

Q55

The vectors a→,b→\overrightarrow{a},\overrightarrow{b} and c→\overrightarrow{c} are of the same length. If taken pairwise, they form equal angles. If a→=i^+j^\overrightarrow{a}=\hat{i}+\hat{j} and b→=j^+k^\overrightarrow{b}=\hat{j}+\hat{k}, then what can c→\overrightarrow{c} be equal to?

I. i^+k^\hat{i}+\hat{k}

II. −i^+4j^−k^3\frac{-\hat{i}+4\hat{j}-\hat{k}}{3}

Select the correct answer using the code given below.

  1. (a) I only
  2. (b) II only
  3. (c) Both I and IICorrect answer
  4. (d) Neither I nor II

Solution.

Answer: (c) Both I and II

  1. Both given vectors have squared length 2 and dot product a·b=1.
  2. Candidate I=(1,0,1) has squared length 2 and dot product 1 with each.
  3. Candidate II=(−1,4,−1)/3 has squared length 18/9=2 and dot products (−1+4)/3=1.
  4. Both candidates meet all conditions.