What is the angle between the following vectors a= 4i+3j+2k and I+2j+5k?

Solutions

Expert Solution

What is the angle between the vectors

a= 4i+3j+2k

and

b=i +2j+5k

To find the angle we need to find the dot product

dot product = 4x1 + 3x2 + 2x5 = 4 + 6 + 10= 20

Next we need to calculate the magnitudes of the vectors

For a

sqrt (4^2 + 3^2 + 2^2) = sqrt (16 + 9 + 4)

=sqrt 29

For b

sqrt ( 1^2 + 2^2 + 5^2 ) = sqrt ( 1 + 4 + 25 )=sqrt 30

So we use the formula

Cos C = dot product/ magnitudes multiplied together

= 20/ ( sqrt29) (sqrt30)

= 20 / ( 5.385 x 5. 477 )

= 20 / 29.49

= 0.6782

Hence C = 47.29 degrees

angle=47.3°

Nipun Maity answered 1 year ago

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