1
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following for the next two (02) items that follow :

Consider two lines whose direction ratios are (2, -1, 2) and (k, 3, 5). They are inclined at an angle $\frac{\pi}{4}$

What are the direction ratios of a line which is perpendicular to both the lines ?
A
(1, 2, 10)
B
(-1, -2, 10)
C
(11, 12, -10)
D
(11, 2, -10)
2
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following for the next two (02) items that follow :

Let $\vec{a}=3 \hat{i}+3 \hat{j}+3 \hat{k} $ and $ \vec{c}=\hat{j}-\hat{k} \text {. Let } \vec{b}$ be such that $\vec{a} \cdot \vec{b}=27 $ and $ \vec{a} \times \vec{b}=\overrightarrow{9 c}$

What is $\vec{b}$ equal to ?
A
$3 \hat{i}+4 \hat{j}+2 \hat{k}$
B
$5 \hat{i}+2 \hat{j}+2 \hat{k}$
C
$5 \hat{i}-2 \hat{j}+6 \hat{k}$
D
$3 \hat{i}+3 \hat{j}+4 \hat{k}$
3
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following for the next two (02) items that follow :

Let $\vec{a}=3 \hat{i}+3 \hat{j}+3 \hat{k} $ and $ \vec{c}=\hat{j}-\hat{k} \text {. Let } \vec{b}$ be such that $\vec{a} \cdot \vec{b}=27 $ and $ \vec{a} \times \vec{b}=\overrightarrow{9 c}$

What is the angle between $(\vec{a}+\vec{b})$ and $\vec{c}$ ?
A
$\frac{\pi}{2}$
B
$\frac{\pi}{3}$
C
$\frac{\pi}{4}$
D
$\frac{\pi}{6}$
4
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following for the item that follow :

Let a vector $\vec{a}=4 \hat{i}-8 \hat{j}+\hat{k}$ make angles α, β, γ with the positive directions of x, y, z axes respectively. 

What is cosα equal to ? 
A
$\frac{1}{3}$
B
$\frac{4}{9}$
C
$\frac{5}{9}$
D
$\frac{2}{3}$
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