Relative to an origin O, the position vectors of points A and B are given byOA = 5i + j + 2k and OB = 2i + 7j + pk,where p is a constant.(i) Find the value of p for which angle AOB is 90◦.

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tiburtius | High School Teacher | (Level 1) Educator

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Two vectors will be perpendicular i.e. at the angle of 90° if their scalar product (dot product) is equal to 0.

So let's find scalar product of those two vectors:

`vec(OA)cdotvec(OB)=5cdot2+1cdot7+2cdotp=17+2p`

Now for those two vectors to be perpendicular `17+2p`  must be equal to 0.

`17+2p=0`

`p=-17/2` <-- Your solution

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