Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Vector Algebra

NDA 2013 · Mathematics · Vector Algebra

If θ is the angle between the vectors 4( i - k ) and i + j + k ,...

If θ\theta is the angle between the vectors 4(i^−k^)4(\hat{i}-\hat{k}) and i^+j^+k^\hat{i}+\hat{j}+\hat{k}, then what is (sin⁡θ+cos⁡θ)(\sin \theta+\cos \theta) equal to?

Options

  1. A00
  2. B12\frac{1}{2}
  3. C11
  4. D22

Correct answer

C. 11

Step-by-step solution

cos⁡θ=4(i^−k^)⋅(i^+j^+k^)=0θ=π2cos⁡θ+sin⁡θ=1\begin{aligned} & \cos \theta=4(\hat{i}-\hat{k}) \cdot(\hat{i}+\hat{j}+\hat{k})=0 \\ & \theta=\frac{\pi}{2} \\ & \cos \theta+\sin \theta=1\end{aligned}
Practice Vector Algebra on Quantrex Academy →

More from Vector Algebra

Passage: Let a × b = c and b × c = a . Question: Consider the following statements : I. (… NDA 2026Passage: Let a , b , c , a + b , b + c , a + b + c be unit vectors. Question: What is the… NDA 2026Passage: Let a , b , c be unit vectors. Further, a is perpendicular to b ; c makes an… NDA 2026Passage: Let a , b , c , a + b , b + c , a + b + c be unit vectors. Question: What is the… NDA 2026Passage: Let a × b = c and b × c = a . Question: Consider the following statements : I. a… NDA 2026Passage: Let a , b , c be unit vectors. Further, a is perpendicular to b ; c makes an… NDA 2026What is the area of the parallelogram whose sides are represented by the vectors i + 2 j… NDA 2025Let p = a - b , q = a + b . If | a | = | b | = 2 and a · b = 2 , then what is the value… NDA 2025A force F = 2 i - λ j + 5 k is applied at the point A(1, 2, 5) . If its moment about the… NDA 2025ABC is a triangle right-angled at B . If A(k, 1, -1) , B(2k, 0, 2) and C(2+2k, k, 1) are… NDA 2025Consider the following statements in respect of a vector d = ( a × b ) × c : I. d is… NDA 2025The position vectors of three points A , B and C are a , b and c respectively such that 3… NDA 2025The position vectors of three points A , B and C are a , b and c respectively, where c =… NDA 2025Let a , b , ( a × b ) be unit vectors. What is ( a · b ) equal to? NDA 2025Let θ be the angle between two unit vectors a and b . If a +2 b is perpendicular to 5 a… NDA 2024What is 3 α+2 β equal to if (2 i +6 j +27 k ) ×( i +α j +β k ) is a null vector? NDA 2024 Full Vector Algebra list Vector Algebra JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs