Question

calculate the dot product of A vector= (-4,-9) and B vector=(-1,2) Do the vector form an acute angle , right angle or , obtuse angle ?
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Answer 1

Answer:

• -14
• obtuse angle

Step-by-step explanation:

You want the dot product of a = (-4, -9) and b = (-1, 2), and the kind of angle between these vectors.

Dot product

The dot product is the sum of the products of corresponding components:

  a•b = (-4)(-1) +(-9)(2) = 4 -18

  a•b = -14

Angle

The angle between the vectors, θ, can be found from ...

  a•b = |a|·|b|·cos(θ)

Then ...

  cos(θ) = (a•b)/(|a|·|b|)

The magnitude of each vector is positive, so the sign of the dot product tells you the sign of the cosine of the angle. For acute angles, the sign is positive; for obtuse angles, it is negative.

The dot product is negative, so the angle between the vectors is obtuse.

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Additional comment

The dot product is zero when the vectors form a right angle, a fact with numerous applications.