VSA

A vector $\vec{a}$ makes equal angles with all the three axes. If the magnitude of the vector is $5\sqrt{3}$ units, then find $\vec{a}$.

MCQ_SINGLE

If a vector makes an angle of $\frac{\pi}{4}$ with the positive directions of both x-axis and y-axis, then the angle which it makes with positive z-axis is :

VSA

Three honey bees were found flying along the vectors $\vec{a}=2\hat{i}-3\hat{j}+\hat{k}$, $\vec{b}=4\hat{j}-2\hat{k}$ and $\vec{c}=3\hat{i}+2\hat{k}$ respectively. Find the value of $\lambda$ such that the path for $\vec{a}+\lambda\vec{b}$ is perpendicular to $\vec{c}$.

MCQ_SINGLE

The value of $(\hat{i}\times\hat{j})\cdot \hat{j}+(\hat{j}\times\hat{i}) \hat{k}:$

SA

The scalar product of the vector $\vec{a}=\hat{i}-\hat{j}+2\hat{k}$ with a unit vector along sum of vectors $\vec{b}=2\hat{i}-4\hat{j}+5\hat{k}$ and $\vec{c}=\lambda\hat{i}-2\hat{j}-3\hat{k}$ is equal to 1. Find the value of $\lambda$.

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