List of top Mathematics Questions on Analytical Geometry asked in IISER

बिन्दु A(\(4\hat{i} + \hat{j} + 3\hat{k}\)), B(\(2\hat{j}\)) तथा C(\(-4\hat{i} + 3\hat{j} - 3\hat{k}\)) के संदर्भ में निम्न कथनों में से कौन सा कथन सत्य है?

Let $l_1$ be the line joining $(1, 1, 1)$ and $(3, 1, 3)$ and let $l_2$ be the line joining $(0, 2, -1)$ and $(2, 0, 3)$. What is the angle between $l_1$ and $l_2$?

Consider the points $A(4\hat{i} + \hat{j} + 3\hat{k})$, $B(2\hat{j})$ and $C(-4\hat{i} + 3\hat{j} - 3\hat{k})$. Which of the following statements is TRUE?

Consider the lines $L_1$ and $L_2$ given below:
$L_1 : x = 2 + \lambda, \quad y = 3 + 2\lambda, \quad z = 4 + 3\lambda$;
$L_2 : x = 4 + \lambda, \quad y = 4, \quad z = 4 + \lambda$.
If $(2, 3, 4)$ is the point of $L_1$ that is closest to $L_2$, then which point of $L_2$ is closest to $L_1$?