Question

Line passing through (3,4,5) and (4,5,6) has direction cosines ......,Select the correct option from the given options.
(a) 1,1,1,1
(b) √3,√3,√3
(c) 1/√3,1/√3/1/√3
(d) 7,9,11

Answer 1

for solution refer attachment answer is option c

Answer 2

if line passing through two points $(a_1,b_1,c_1)$ and $(a_2,b_2,c_2)$
then, direction cosine of lines are $\{\frac{(a_2-a_1)}{\sqrt{(a_2-a_1)^2+(b_2-b_1)^2+(c_2-c_1)^2}},\frac{(b_2-b_1)}{\sqrt{(a_2-a_1)^2+(b_2-b_1)^2+(c_2-c_1)^2}},\frac{(c_2-c_1)}{\sqrt{(a_2-a_1)^2+(b_2-b_1)^2+(c_2-c_1)^2}}\}$

here, $a_1=3,b_1=4,c_1=5$ and $a_2=4,b_2=5,c_2=6$

now, direction cosine :
$\{\frac{(4-3)}{\sqrt{(4-3)^2+(5-4)^2+(6-5)^2}},\frac{(5-4)}{\sqrt{(4-3)^2+(5-4)^2+(6-5)^2}},\frac{(6-5)}{\sqrt{(4-3)^2+(5-4)^2+(6-5)^2}}$

$\{\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}\}$

hence, option (c) is correct.