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

The condition for the lines with direction ratio a_1,b_1,c_1 and a_2,b_2,c_2 are perpendicular is -

Let a, b and c be non-zero vectors such that (vecaxxvecb)xxvecc=(-1)/(4)|vecb||vecc|veca . If theta the acute angle between the vectors b and c, then the angle between a and c is equal to

Find the area of a triangle whose sides are a and b and the angle between those sides is C

If a, b, c are positive and unequal show that value of the determinant Delta=|[a, b, c],[ b, c, a],[ c, a, b]| is negative.

Find the value of the determinant |[1, a, b+c],[ 1, b, c+a],[ 1, c, a+b]|