1
NDA Mathematics 10 April 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
If $4\hat i + \hat j - 3\hat k$ and $p\hat i + q\hat j - 2\hat k$ are collinear vectors, then what are the possible values of p and q respectively?
A
4, 1
B
1, 4
C
$\frac{8}{3}, \frac{2}{3}$
D
$\frac{2}{3}, \frac{8}{3}$
2
NDA Mathematics 10 April 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
If $\vec a, \vec b, \vec c$, are the position vectors of the vertices A, B, C respectively of a triangle ABC and G is the centroid of the triangle, then what is $\overrightarrow{AG}$ equal to ? .
A
$\frac{\vec a + \vec b +\vec c}{3}$
B
$\frac{2\vec a - \vec b -\vec c}{3}$
C
$\frac{\vec b + \vec c - 2\vec a}{3}$
D
$\frac{\vec a - 2\vec b - 2\vec c}{3}$
3
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
4
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
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