# Vector Algebra · Mathematics · NDA

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NDA Mathematics 21 April 2024
If the direction cosines <l, m, n> of a line are connected by relation $l + 2m + n = 0, 2l - 2m + 3n = 0$, then what is the value of $l^{2} + m^... NDA Mathematics 21 April 2024 Let$\vec{a} = \hat{i} - \hat{j} + \hat{k}$and$\vec{b} = \hat{i} + 2\hat{j} - \hat{k}$. If$\vec{a} \times (\vec{b} \times \vec{a}) = \alpha \hat{i}...
NDA Mathematics 21 April 2024
If a vector of magnitude 2 units makes an angle $\frac{\pi}{3}$ with $2\hat{i}$, $\frac{\pi}{4}$ with $3\hat{j}$ and an acute angle $\theta$ with $4\h... NDA Mathematics 21 April 2024 Consider the following in respect of moment of a force:1. The moment of force about a point is independent of point of application of force.2. The mom... NDA Mathematics 21 April 2024 For any vector$\vec{r}$, what is$\left(\vec{r}\cdot\hat{i}\right)\left(\vec{r}\times\hat{i}\right) + \left(\vec{r}\cdot\hat{j}\right)\left(\vec{r}\t...
NDA Mathematics 21 April 2024
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 $\vec{a} ... NDA Mathematics 3 September 2023 What is the length of projection of the vector$\rm \hat{i}+2 \hat{j}+3 \hat{k}$on the vector$\rm2 \hat{i}+3 \hat{j}-2 \hat{k}$?... NDA Mathematics 3 September 2023 If$\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}|$... NDA Mathematics 3 September 2023 If θ is the angle between vectors$\vec{a}$and$ \vec{b}$such that$\vec{a} \cdot \vec{b} \geq 0$, then which one of the following is... NDA Mathematics 3 September 2023 The vectors$\rm 60 \hat{i}+3 \hat{j}, 40 \hat{i}-8 \hat{j}$and$\rm \beta \hat{i}-52 \hat{j}$are collinear if :... NDA Mathematics 3 September 2023 Consider the following in respect of the vectors$\rm \vec{a}=(0,1,1)$and$\rm \vec{b}=(1,0,1) $: 1. The number of unit&nb... NDA Mathematics 16 April 2023 What is$\vec{b}$equal to ? NDA Mathematics 16 April 2023 What is the angle between$(\vec{a}+\vec{b})$and$\vec{c}$? NDA Mathematics 16 April 2023 What is cosα equal to ? NDA Mathematics 16 April 2023 What is cos2β + cos2γ equal to ? NDA Mathematics 16 April 2023 Consider the following points : 1. (-1, -3, 1) 2. (-1, 3, 2) 3. (-2, 5, 3) Which of the above points lie on the line joining A ... NDA Mathematics 16 April 2023 What is the magnitude of$\overrightarrow{A B}\$ ?
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