Vectors · NDA previous year questions

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2026 6 questions

Q992026 · 12 Apr 2026
Passage: Let $a, b, c$ be unit vectors. Further, $a$ is perpendicular to $b$ ; $c$ makes an angle $\frac{π}{3}$ with both $a$ and $b$ ; and $c = p a + q b + r (a \times b)$ . Question: What is the value of $r^{2}$ ?
1. A.4
2. B.2
3. C.1
4. D. $\frac{1}{2}$
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Answer: D
Q1002026 · 12 Apr 2026
Passage: Let $a, b, c$ be unit vectors. Further, $a$ is perpendicular to $b$ ; $c$ makes an angle $\frac{π}{3}$ with both $a$ and $b$ ; and $c = p a + q b + r (a \times b)$ . Question: What is the value of $(p + q)$ ?
1. A. $\frac{1}{2}$
2. B.1
3. C. $\frac{3}{2}$
4. D.2
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Answer: B
Q1012026 · 12 Apr 2026
Passage: Let $a \times b = c$ and $b \times c = a$ . Question: Consider the following statements : I. $(a \times b) \cdot c + (b \times c) \cdot a = (c \times a) \cdot b$ II. ${(a \times b) \times (b \times c)} \cdot b = 1$ Which of the statements given above is/are correct ?
1. A.I only
2. B.II only
3. C.Both I and II
4. D.Neither I nor II
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Answer: D
Q1022026 · 12 Apr 2026
Passage: Let $a \times b = c an d b \times c = a$ . Question: Consider the following statements : I. $a, b, c$ are orthogonal in pairs. II. $a, b, c$ are unit vectors. Which of the statements given above is/are correct ?
1. A.I only
2. B.II only
3. C.Both I and II
4. D.Neither I nor II
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Answer: A
Q1032026 · 12 Apr 2026
Passage: Let $a, b, c, a + b, b + c, a + b + c$ be unit vectors. Question: What is the angle between $a$ and $c$ ?
1. A. $\frac{π}{6}$
2. B. $\frac{π}{4}$
3. C. $\frac{π}{2}$
4. D. $\frac{2 π}{3}$
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Answer: C
Q1042026 · 12 Apr 2026
Passage: Let $a, b, c, a + b, b + c, a + b + c$ be unit vectors. Question: What is the angle between $a$ and $b$ ?
1. A. $\frac{π}{6}$
2. B. $\frac{π}{4}$
3. C. $\frac{π}{2}$
4. D. $\frac{2 π}{3}$
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Answer: D