1
NDA 2019 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
The sine of the angle between vectors $$a = 2\widehat i - 6\widehat j - 3\widehat k$$ and $$b = 4\widehat i + 3\widehat j - \widehat k$$ is
A
$${1 \over {\sqrt {26} }}$$
B
$${5 \over {\sqrt {26} }}$$
C
$${5 \over {26}}$$
D
$${1 \over {26}}$$
2
NDA 2019 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
What is the value of $$\lambda$$ for which the vectors $$3\widehat i + 4\widehat j - \widehat k$$ and $$ - 2\widehat i + \lambda \widehat j + 10\widehat k$$ are perpendicular?
A
1
B
2
C
3
D
4
3
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

If the direction cosines <l, m, n> of a line are connected by relation $l + 2m + n = 0, 2l - 2m + 3n = 0$, then what is the value of $l^{2} + m^{2} - n^{2}$?

A

$\frac{1}{101}$

B

$\frac{29}{101}$

C

$\frac{41}{101}$

D

$\frac{92}{101}$

4
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Let $\vec{a} = \hat{i} - \hat{j} + \hat{k}$ and $\vec{b} = \hat{i} + 2\hat{j} - \hat{k}$. If $\vec{a} \times (\vec{b} \times \vec{a}) = \alpha \hat{i} - \beta \hat{j} + \gamma \hat{k}$, then what is the value of $\alpha + \beta + \gamma$?

A

8

B

7

C

6

D

1

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