NDA Mathematics 21 April 2024 | Vector Algebra Question 64 | Mathematics

Let $\vec{a}$ and $\vec{b}$ be two vectors of magnitude 4 inclined at an angle $\frac{\pi}{3}$, then what is the angle between $\vec{a}$ and $\vec{a} - \vec{b}$?

$\frac{\pi}{2}$

$\frac{\pi}{3}$

$\frac{\pi}{4}$

$\frac{\pi}{6}$

NDA Mathematics 3 September 2023

MCQ (Single Correct Answer)

+2.5

-0.83

What is the length of projection of the vector $\rm \hat{i}+2 \hat{j}+3 \hat{k}$ on the vector $\rm2 \hat{i}+3 \hat{j}-2 \hat{k}$ ?

$\frac{1}{\sqrt{17}}$

$\frac{2}{\sqrt{17}}$

$\frac{3}{\sqrt{17}}$

$\frac{2}{\sqrt{14}}$

NDA Mathematics 3 September 2023

MCQ (Single Correct Answer)

+2.5

-0.83

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 $\rm|\vec{a}|$ ?

NDA Mathematics 3 September 2023

MCQ (Single Correct Answer)

+2.5

-0.83

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?

0 ≤ θ ≤ π

$\frac{\pi}{2} \leq \theta \leq \pi$

$0 \leq \theta \leq \frac{\pi}{2}$

$0<\theta<\frac{\pi}{2}$

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