Question

Question 1: Direction ratios of a line are 2, 3,-6. Then direction cosines of a line
making obtuse angle with the y-axis are
a) 2/7,-3/7,-6/7
b) -2/7,3/7,-6/7
c) -2/7,-3/7,6/7
d) -2/7,-3/7,-6/7​

Answer 1

Answer:

answer:c

Step-by-step explanation:

(c), as direction cosines of a line whose direction ratio are 2,3, -6 are 27,37,−67.

As angle with the y-axis is obtuse,

∴ cos β < 0,

Therefore direction ratios are −27,−37,67.

Answer 2

Answer:

The correct answer is Option C

Step-by-step explanation:

If the direction ratios are given as x,y,z, then the direction cosines are given by

$\frac{x}{\sqrt{x^2+y^2+z^2}}, \frac{y}{\sqrt{x^2+y^2+z^2}}, \frac{z}{\sqrt{x^2+y^2+z^2}}$

So, the direction cosines for direction ratios 2,3,-6 are  

$\frac{2}{\sqrt{2^2+3^2+(-6)^2}}, \frac{3}{\sqrt{2^2+3^2+(-6)^2}}, \frac{-6}{\sqrt{2^2+3^2+(-6)^2}}$

$\frac{2}{\sqrt{4+9+36}}, \frac{3}{\sqrt{4+9+36}}, \frac{-6}{\sqrt{4+9+36}}\\\\\frac{2}{\sqrt{49} } , \frac{3}{\sqrt{49} } , \frac{-6}{\sqrt{49} } \\\frac{2}{7} , \frac{3}{7} , \frac{-6}{7}$

As direction cosines of a line whose direction ratio are 2,3, -6 are 2/7,3/7,−6/7. As angle with the y-axis is obtuse, ∴ cos β < 0, Therefore direction ratios are -2/7,-3/7,6/7.