# Relative to an origin O, the position vectors of points A and B are 3i + 4j − k and 5i − 2j − 3k respectively.Use a scalar product to find angle BOA.

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Relative to an origin O, the position vectors of points A and B are 3i + 4j − k and 5i − 2j − 3k respectively.

Use a scalar product to find angle BOA.

vector OA=3i+4j-k

vector OB= 5i-2j -3k

Let angle between OA ana OB be `theta`

Thus

`OA.OB= |OA||OB| cos(theta)`

`(15-8+3)=sqrt(9+16+1)sqrt(25+4+9)cos(theta)`

`10/sqrt(988)=10/31.43=.318`

`theta=cos^(-1)(0.318)`

`theta=71.45^o`