Let vector a = x^2 i + 2j - 2k, vector b= i - j + k and vector c= x^2i + 5j - 4k be three vectors. find the values of x for which the angle

Question

Let  \(\vec a=\text x^2\hat i+2\hat j-2\hat k\),  \(\vec b= \hat i-\hat j+\hat k\)  and  \(\vec c=\text x^2\hat i+5\hat j-4\hat k\)  be three vectors. Find the values of x for which the angle between  \(\vec a\) and  \(\vec b\) is obtuse

Answer 1

We know that,

\(\vec a.\vec b=|\vec a||\vec b|\) cos x

Where, x is the angle between two vectors

Applying for  \(\vec a\) and  \(\vec b\)

Since angle between  \(\vec a\) and  \(\vec b\) is acute cos x should be greater than 0

Since angle between  \(\vec c\) and  \(\vec b\) is obtuse cos x should be less than 0