Find angle between the two lines whose direction ratios are 1,-2,1 and 4,3,2 respectively

(i) Find the angle bewteen the lines whose direction ratios are 1, 2, 3 and - 3 , 2 , 1 (ii) Find the angle between two diagonals of a cube.

STATEMENT-1 : The angle between the lines whose direction ratios are (1, 2, 3) and (-12, 3, 2) is 90^(@) STAEMENT-2 : The direction cosines of a line whose direction ratios are (3, 4, 12) are (3/13, 4/13, 12/13) . STATEMENT-3 : If cosalpha, cosbeta,cosgamma are the direction cosines of a line then sin^(2)alpha + sin^(2)beta +sin^(2)gamma = 2.

Find the angle between the lines whose direction ratios are a, b, c and b - c , c - a , a - b .

Find the angle between the vectors with direction ratios proportional to 1,-2,1 and 4,3, 2.

Find the angle between the lines whose direction ratios are proportional a ,b ,c and b-c ,c-a ,a-bdot

Find the angle between the lines whose direction ratios are proportional a ,b ,c and b-c ,c-a ,a-bdot

Find the angle between two lines whose direction ratios are proportional to 1,1,2a n d(sqrt(3)-1),(-sqrt(3)-1),4 .

Find the angle between those lines whose direction ratios are as follows : (i) (2,3,6) and (1,2,2) (ii) (4,-3,5) and (3,4,5) (iii) (1,2,1) and (4,-3,2)

Find the angel between the vectors with direction ratios proportional to 1, -2, 1 and 4, 3, 2.

Find the angle between the lines whose slopes are -3 and -1/(2) .