1
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
2
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

$\frac{92}{101}$

3
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

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

If a vector of magnitude 2 units makes an angle $\frac{\pi}{3}$ with $2\hat{i}$, $\frac{\pi}{4}$ with $3\hat{j}$ and an acute angle $\theta$ with $4\hat{k}$, then what are the components of the vector?

A

(1, $\sqrt{2}$, 1)

B

(1, $-\sqrt{2}$, 1)

C

(1, $-\sqrt{2}$, -1)

D

(1, $\sqrt{2}$, -1)

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