(i) If a line in the space makes angle α, β and γ with the coordinates axes, then cos^2α + cos^2β + cos^2γ is equal to

Question

Choose the correct answer from the bracket,
(i) If a line in the space makes angle α, β and γ with the coordinates axes, then cos²α + cos²β + cos²γ is equal to

(a) 1

(b) 2

(c) 0

(d) 3

(ii) The direction ratios of the line are \(\frac{x-6}{1} = \frac{2-y}{2} = \frac{z-2}{2}\)

(a) 6, -2, -2

(b) 1, 2, 2

(c) 6, 1, -2

(d) 0, 0, 0

(iii) If the vector equation of a line is \(\bar r\) = i + j + k + µ(2i – 3j – 4k), then the Cartesian equation of the line

(iv) If the Cartesian equation of a plane is x + y + z =12, then the vector equation of the line is  

(a) \(\bar r\).(2i + j + k) = 12 

(b) \(\bar r\).(i + j + k) = 12

(c) \(\bar r\).(i + y + 2k) = 12 

(d) \(\bar r\).(i + 3j + k) = 12

Answer 1

(i) (a) 1 

(ii) (b) 1, 2, 2 

(iii) (b) \(\frac{x-1}{2} = \frac{y-1}{-3} = \frac{z-1}{-4}\) 

(iv) (b) \(\bar r\).(i + j + k) = 12.