1
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
If $\rm (\vec{a} \times \vec{b})^2+(\vec{a} \cdot \vec{b})^2=144$ and $\rm|\vec{b}|=4 $, then what is the value of $\rm|\vec{a}|$ ?
A
3
B
4
C
5
D
6
2
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
If θ is the angle between vectors $\vec{a}$ and $ \vec{b}$ such that $\vec{a} \cdot \vec{b} \geq 0$, then which one of the following is correct?
A
0 ≤ θ ≤ π 
B
$\frac{\pi}{2} \leq \theta \leq \pi$
C
$0 \leq \theta \leq \frac{\pi}{2}$
D
$0<\theta<\frac{\pi}{2}$
3
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
The vectors $\rm 60 \hat{i}+3 \hat{j}, 40 \hat{i}-8 \hat{j}$ and $\rm \beta \hat{i}-52 \hat{j}$ are collinear if :
A
β = 20
B
β = 40
C
β = -40
D
β = 26
4
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following in respect of the vectors $\rm \vec{a}=(0,1,1)$ and $\rm \vec{b}=(1,0,1) $ :

1. The number of unit vectors perpendicular to both $\rm \vec{a}$ and $\rm \vec{b}$ is only one.

2. The angle between the vectors is $\frac{\pi}{3}$.

Which of the statements given above is/are correct?

A
1 only
B
2 only
C
Both 1 and 2
D
Neither 1 nor 2
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