1
NDA Mathematics 10 April 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following statements :

1. Dot product over vector addition is distributive

2. Cross product over vector addition is distributive

3. Cross product of vectors is associative

Which of the above statements is/are correct ?

A
1 only
B
2 only
C
1 and 2 only
D
1, 2 and 3
2
NDA Mathematics 10 April 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Let  $\vec{a}, \vec{b}, \vec{c}$ be three non-zero vectors such that  $\vec{a}\times \vec{b} = \vec{c} $. Consider the following statements:

1. $\vec a$ is unique if $\vec b$ and $\vec c$ are given

2. $\vec c$ is unique if $\vec a$ and $\vec b$ are given

Which of the above statements is/are correct?

A
1 only
B
2 only
C
Both 1 and 2
D
Neither 1 nor 2
3
NDA Mathematics 10 April 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
Let $\vec a$ and $\vec b$ be two unit vectors such that $|\vec a - \vec b|<2.$ If 2θ is the angle between $\vec a$ and $\vec b,$ then which one of the following is correct ?
A
0 ≤ sin θ < 1 only
B
$-\frac{1}{2} < \sin \theta < \frac{1}{2} \ \text{only}$
C
-1 < sin θ < 0 only
D
-1 < sin θ < 1
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