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 :

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
$\frac{\pi}{6}$
2
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
$\frac{2}{3}$
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 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 cos2β + cos2γ equal to ? 
A
$-\frac{32}{81}$
B
$-\frac{16}{81}$
C
$\frac{16}{81}$
D
$\frac{32}{81}$
4
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 :

The position vectors of two points A and B are î - ĵ and ĵ + k̂ respectively. 

Consider the following points :

1. (-1, -3, 1)

2. (-1, 3, 2)

3. (-2, 5, 3)

Which of the above points lie on the line joining A and B ?  

A
1 and 2 only 
B
2 and 3 only 
C
1 and 3 only 
D
1, 2 and 3 
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