the acute angle in degrees that makes a with c, when a=4i+0j+k , c=i+j+3k

Guest Aug 27, 2014

#1**+10 **

We need to find two things here, the dot product of the two vectors and the magnitude of each.

The dot product is <4, 0, 1 > (dot) < 1, 1, 3 > = (4 + 0 + 3) = 7

The magnitude of a = √(4^{2} + 0^{2} + 1^{2}) =√(16 + 1) = √17

And the magnitude of c = √(1^{2} + 1^{2} + 3^{2}) =√(1 + 1 + 9) = √11

And the angle is given by

cos^{-1} (a(dot)c / (llall * llcll) = cos^{-1} ((7) / (√17 * √11) = cos^{-1} ((7) / (√187) = cos^{-1} (0.5118906968889915) = about 59.2°

CPhill Aug 27, 2014

#1**+10 **

Best Answer

We need to find two things here, the dot product of the two vectors and the magnitude of each.

The dot product is <4, 0, 1 > (dot) < 1, 1, 3 > = (4 + 0 + 3) = 7

The magnitude of a = √(4^{2} + 0^{2} + 1^{2}) =√(16 + 1) = √17

And the magnitude of c = √(1^{2} + 1^{2} + 3^{2}) =√(1 + 1 + 9) = √11

And the angle is given by

cos^{-1} (a(dot)c / (llall * llcll) = cos^{-1} ((7) / (√17 * √11) = cos^{-1} ((7) / (√187) = cos^{-1} (0.5118906968889915) = about 59.2°

CPhill Aug 27, 2014