Question

solve this and show how #vectors class 12

Answer 1

Q. A vector makes an angle of 90°, 105°,45° with positive directions of X, Y, Z axis. Find direction ratios

Sol. Direction ratios comes from the more basic idea of direction cosines.
=>Direction cosines are the cosines of angles made by a vector with coordinate axes.

=>So, Here direction cosines are

$l = \cos90 = 0 \\ m = \cos135 = \frac{ - 1}{ \sqrt{2} } \\ n = \cos45 = \frac{1}{ \sqrt{2} }$

Here, l, m, n are direction cosines

=>When any constant is multiplied with the direction cosines, they are called direction ratios.

So, λl, λm, λn,are direction ratios where λ=constant

$answer = > lamda(0) \: lamda( \frac{ - 1}{ \sqrt{2} } ) \: lamda( \frac{1}{ \sqrt{2} } )$
=>Direction ratios help in Simplifying calculations.
For example, if we take x= root 2, then direction ratios becomes 0,-1, 1.
Hence, calculation becomes easier with these.