Scaler product of two vectors

Geometry Level pending

Points A A and B B have position vectors a ⃗ \vec a and b ⃗ \vec b relative to the origin of coordinates. They lie on a straight line p x = q y = r z px=qy=rz . What is the value of a ⃗ . b ⃗ \vec a. \vec b ?

a 2 − a b + b 2 a^2-ab+b^2 a 2 + b 2 a^2+b^2 a 2 + a b + b 2 a^2+ab+b^2 a b ab

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1 solution

The straight line p x = q y = r z px=qy=rz passes through the origin. Therefore the vectors a ⃗ \vec a and b ⃗ \vec b are collinear, and hence a ⃗ . b ⃗ = a b \vec a. \vec b=ab .

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