Column Matching:
Column –I | Column –II |
(i) Angle between two diagonals of a cube | [A] cos–1 |
(ii) Angle between one diagonal of a cube and a diagonal of one face | [B] cos–1 |
(iii) Angle between the Rays with d.r.'s 4, – 3, 5 & 3, 4, 5 | [C] cos–1 |
(iv) A line OP through origin O is inclined at 30º and 45º to OX and OY respectively. The angle at which it is inclined to OZ is | [D] Not defined |
Text Solution
Verified by Experts(i) [B]; (ii) [C]; (iii) [A]; (iv) [D]
Ans.
(i) [B]
(ii) [C]
(iii) [A]
(iv) [D]
Sol. (i) Angle between two diagonals of a cube = cos–1 
(ii) Angle between the diagonal of a cube and a diagonal of one face = cos–1 
(iii) cos θ = 
= 
= 
θ = cos–1 
(iv) Let λ , m, n be the direction cosines of the given
vector, then λ 2 + m2 + n2 =1. If λ = cos 30º= 
,
m = cos 45º = 
, then 
+ 
+ n2 =1,
⇒ n2 = – 
which is not possible.
So, such a line cannot exist.)
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