NDA Mathematics 4 September 2022 | Vector Algebra Question 21 | Mathematics

What are the values of x for which the angle between the vectors 2x²$\hat{\text{i}}$ + 3x$\hat{\text{j}}$ + $\hat{\text{k}}$ and $\hat{\text{i}}$ −2$\hat{\text{j}}$ + x²$\hat{\text{k}}$ is obtuse ?

0 < x < 2

x < 0

x > 2

0 ≤ x ≤ 2

NDA Mathematics 4 September 2022

MCQ (Single Correct Answer)

+2.5

-0.83

The position vectors of vertices A, B and C of triangle ABC are respectively $\hat{\text{j}}+\hat{\text{k}}, 3\hat{\text{i}}+\hat{\text{j}+5\hat{\text{k}}}$ and $3\hat{\text{j}}+3\hat{\text{k}}$. What is angle C equal to?

$\frac{\pi}{6}$

$\frac{\pi}{4}$

$\frac{\pi}{3}$

$\frac{\pi}{2}$

NDA Mathematics 10 April 2022

MCQ (Single Correct Answer)

+2.5

-0.83

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?

4, 1

1, 4

$\frac{8}{3}, \frac{2}{3}$

$\frac{2}{3}, \frac{8}{3}$

NDA Mathematics 10 April 2022

MCQ (Single Correct Answer)

+2.5

-0.83

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 ? .

$\frac{\vec a + \vec b +\vec c}{3}$

$\frac{2\vec a - \vec b -\vec c}{3}$

$\frac{\vec b + \vec c - 2\vec a}{3}$

$\frac{\vec a - 2\vec b - 2\vec c}{3}$

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