Question

Find the angle between the two vectors A = 2i + 4j – 2k and B = 3i – 5j + k.

Answer 1

131 ° is the angle between the two vectors

Explanation:

for 2 vectora a and b  having  θ angle between them , the cos of angle between themis given by

cos θ= $\frac{a .b }{|a| |b| }$

now

a.b = 2*3 + 4*-5 + -2*1

    = 6+-20-2

   = -16

|a| = $\sqrt{2*2 + 4*4+ -2*-2}$

  = $\sqrt{4 + 16+4 }$

 = $\sqrt{24}$

|b| =

$\sqrt{3*3 + -5*-5 + 1*1 \\} \\\sqrt{35 }$

cos θ= $\frac{a .b }{|a| |b| }$

        = -16 / ($\sqrt{24}$ * $\sqrt{35}$ )

     = -16 / 24.39

   = - 0.655

θ= cos⁻¹ (-0.655 )

= 131 °