Question

which of the following statements is/are TRUE?

Answer 1

ANSWER.

Option [ A ] and [ B ] is correct answer.

EXPLANATION.

$\sf : \implies \: l_{1} \: and \: l_{2} \: \: are \: \: straight \: \: lines \\ \\ \sf : \implies \: l_{1} \: = \frac{x - 1}{1} = \frac{y}{ - 1} = \frac{ z - 1 }{3} \\ \\ \sf : \implies \: l_{2} \: = \frac{x - 1}{ - 3} = \frac{y}{ - 1} = \frac{z - 1}{3}$

$\sf : \implies \: intersection \: points \: are \: (1 ,0 ,1) \\ \\ \sf : \implies \: we \: can \: find \: angle \: bisector \: in \: two \: lines \\ \\ \sf : \implies \: l_{1} = d_{1} \: = \hat{i} - \hat{j} + 3 \hat{k} \\ \\ \sf : \implies \: l_{2} \: = d_{2} \: = - 3 \hat{i} - \hat{j} + \hat{k} \\ \\ \sf : \implies \: dot \: products \: of \: these \: two \: lines \: \\ \\ \sf : \implies \: d_{1}. d_{2} \: = (\hat{i} - \hat{j} + 3 \hat{k})( - 3 \hat{i} - \hat{j} + \hat{k}) \\ \\ \sf : \implies \: d_{1}. d_{2} \: = - 3 + 1 + 3 = 1 = accute \: angles$

$\sf : \implies \: addition \: of \: the \: vector \: \\ \\ \sf : \implies \: d_{1} + d_{2} \: = ( \hat{i} - \hat{j} + 3 \hat{k}) + ( - 3 \hat{i} - \hat{j} + \hat{k}) \\ \\ \sf : \implies \: d_{1} + d_{2} \: = - 2 \hat{i} \: - 2 \hat{j} + 4 \hat{k} \\ \\ \sf : \implies \: d_{1} + d_{2} \: it \: is \: written \: as \: = (1 , 1 , - 2)$

$\sf : \implies \: suppose \: the \: line \: is \: \\ \\ \sf : \implies \: l \: = \frac{x - \alpha }{l} = \frac{y - 1}{m} = \frac{z - \gamma }{ - 2} \\ \\ \sf : \implies \: point \: are \: = ( \alpha , 1, \beta ) \\ \\ \sf : \implies \: \alpha - 1 = 1 = \frac{y - 1}{2}$

$\sf : \implies \: \alpha - 1 = 1 \\ \\ \sf : \implies \: \alpha = 2 \\ \\ \sf : \implies \: \frac{y - 1}{ - 2} = 1 \\ \\ \sf : \implies \: y \: = - 1 \\ \\ \sf : \implies \: it \: satisfied \: the \: equation \\ \\ \sf : \implies \: l + m \: = 2 \: \: \: and \: \: \: \alpha - \gamma = 3$