If for all real x the vector `cxhati-6hatj+3hatk and xhati+2hatj+2cxhatk` makes an obtuse angle with one another then find the value of c

Determine the value of c so that for the real x, vectors cx hati - 6 hatj - 3 hatk and xhati + 2hatj + 2cx hatk make an obtuse angle with each other .

The value of c so that for all real x, the vectors cxhatk + 3hatj, xhati + 2hatj + 2cx hatk make an obtuse angle are:

Find the angle between the vectors hati-2hatj+3hatk and 3hati-2hatj+hatk .

Find the angle between the vectors 4hati-2hatj+4hatk and 3hati-6hatj-2hatk.

If vectors ax hati+3hatj-5hatk and xhati+2hatj+2axhatk make an acute angle with each other, for all x in R then a belongs to the interval

If the vectors vecb = tanalpha hati = hatj+2, sqrt(sinalpha/2hatk) , and vecc=tan alpha hati + tan alpha hatj-3/sqrt(sin alpha/2)hatk are orthogonal and a vector veca = hati + 3hatj + sin 2alpha hatk makes an obtuse angle with the z-axis, then the value of alpha is

A vector vecc of magnitude sqrt(7) which is perpendicular to the vector veca=2hatj-hatk and vecb=-hati+2hatj-3hatk and makes an obtuse angle with the y-axis is given by

If the vectors xhati - 3hatj + 7 hatk and hati + y hatj- z hatk are colliner then the value of (xy^(2))/(z) is equla .