SOLUTION:
WE ALREADY KNOW THAT DOT OR SCALAR PRODUCT OF VECTORS IS DEFINED
AS a.b =mod(a) mod(b) COS\Theta
the value of COS \Theta decides the sign of a.b { since mod(a) and mod(b) are always positive}
IF COS\Theta IS POSITIVE a.b is also positive and if COS\Theta is negative then a.b is also
negative and vice versa.THUS, If a.b is negative COS\Theta is negative and \Theta is obtuse.
If a.b is positive COS\Theta is positive and \Theta is acute.
WE WILL USE THE ABOVE STATED IDEA TO SOLVE THE GIVEN PROBLEM.
in our problem, a=xi-3j-k and b=2xi+xj-k
thus a.b=2x^2-3x+1
2x^2-3x+1 is a quadratic polynomial which is always positive for all values of x.
(Hint:find discriminant of quadratic polynomial)
SINCE a.b is positive COS\Theta IS POSITIVE and \Theta is acute.Thus angle between vectors a and b is acute for all valurs of x.
Y-axis can be represented in vector form by \pmj
If we talk about positive Y-axis then +j otherwise -j.
IN THE QUESTION POSITIVE OR NEGATIVE Y-axis is not mentioned .hence we are taking positive Y-axis.
IF the angle between positive Y-axis and vector b is obtuse the b.j must be negative
here b.j= x
THUS ANGLE BETWEEN Y-AXIS AND VECTOR b IS OBTUSE FOR ALL x
