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 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
$\frac{32}{81}$
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 :

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 
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 :

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

What is the magnitude of $\overrightarrow{A B}$ ?
A
2
B
3
C
√6
D
√3
4
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
PQRS is a parallelogram. If $\overrightarrow{\text{PR}}=\vec{\text{a}}$ and $\overrightarrow{\text{QS}}=\vec{\text{b}}$, then what is $\overrightarrow{\text{PQ}}$ equal to ?
A
$\vec{\text{a}}+\vec{\text{b}}$
B
$\vec{\text{a}}−\vec{\text{b}}$
C
$\frac{\vec{\text{a}}+\vec{\text{b}}}{2}$
D
$\frac{\vec{\text{a}}−\vec{\text{b}}}{2}$
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