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NDA 2025
Exam
NDA
Year
2025
Subject
Mathematics
Chapter
Vector Algebra

NDA 2025 · Mathematics · Vector Algebra

Let a , b , ( a × b ) be unit vectors. What is ( a · b ) equal to?

Let a⃗\vec{a}, b⃗\vec{b}, (a⃗×b⃗)(\vec{a} \times \vec{b}) be unit vectors. What is (a⃗⋅b⃗)(\vec{a} \cdot \vec{b}) equal to?

Options

  1. A00
  2. B12\dfrac{1}{2}
  3. C11
  4. D33

Correct answer

A. 00

Step-by-step solution

Given ∣a⃗∣=1|\vec{a}| = 1, ∣b⃗∣=1|\vec{b}| = 1, and ∣a⃗×b⃗∣=1|\vec{a} \times \vec{b}| = 1.

Using Lagrange's identity, ∣a⃗×b⃗∣2+(a⃗⋅b⃗)2=∣a⃗∣2∣b⃗∣2|\vec{a} \times \vec{b}|^2 + (\vec{a} \cdot \vec{b})^2 = |\vec{a}|^2 |\vec{b}|^2.

Substituting the given values, 12+(a⃗⋅b⃗)2=12×121^2 + (\vec{a} \cdot \vec{b})^2 = 1^2 \times 1^2.

1+(a⃗⋅b⃗)2=11 + (\vec{a} \cdot \vec{b})^2 = 1.

(a⃗⋅b⃗)2=0⇒a⃗⋅b⃗=0(\vec{a} \cdot \vec{b})^2 = 0 \Rightarrow \vec{a} \cdot \vec{b} = 0.

Answer: 00
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