Question

Angle between vectot A=2i cap+j cap-k cap and vector B=i cap-k cap

Answer 1

Magnitude of A: √(2²+1²+(-1)²)=√6

Magnitude of B: √(1²+(-1²))=√2

$ABcos\alpha =A . B\\\sqrt{6} *\sqrt{2} *cos\alpha =(2i+1j-1k)*(1i-1k)\\\sqrt{12}cos\alpha =2+0+1\\cos\alpha =3/\sqrt{12}\\ cos\alpha =\frac{\sqrt{3} }{\sqrt{4}}\\\alpha =cos^{-1}(\sqrt{3}/ 2 )\\\alpha =30 deg$