What is the angle between $<-4,3,-8 >$ and $< 6,-3,8 >$ ?

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Answer 1 · 2016-10-19T10:07:07

Angle between $< -4,3,-8>$ and $< 6,-3,8>$ is $170.01^o$

Angle between two vectors $vecu=a_1hati+b_1hatj+c_1hatk$ or $< a_1,b_1,c_1>$

and $vecv=a_2hati+b_2hatj+c_2hatk$ or $< a_2,b_2,c_2>$ is given by

$costheta=((vecu*vecv))/((|vecu|*|vecv|))$ ,

where $vecu*vecv=a_1a_2+b_1b_2+c_1c_2$

and $|vecu|$ or $|vecv|$ are magnitudes of vectors $vecu$ or $vecv$ and here they are

$sqrt(a_1^2+b_1^2+c_1^2)$ and $sqrt(a_2^2+b_2^2+c_2^2)$

Hence angle between $< -4,3,-8>$ and $< 6,-3,8>$ is given by

$costheta=((-4)xx6+3xx(-3)+(-8)xx8)/(sqrt((-4)^2+3^2+(-8)^2)xxsqrt(6^2+(-3)^2+8^2))$

= $(-24-9-64)/(sqrt(16+9+64)xxsqrt(36+9+64))$

= $-97/(sqrt89xxsqrt109)$

= $-97/(9.43398xx10.44031)$

= $-0.9848$

and $theta=170.01^o$

What is the angle between <-4,3,-8 ><-4,3,-8 > and < 6,-3,8 >< 6,-3,8 >?