Two vectors with magnitudes of 6 and 9 have a dot product equal to –27. Find the angle between the vectors.

120°

Step-by-step explanation:

From the question,

The expression for the dot product of two vector is given as

a.b = abcosθ Equation 1

make θ the subject of the equation

θ =cos⁻¹ (a.b/ab) Equation 2

Where θ = angle between the vector.

Given: a.b = -27, a = 6, b = 9

Substitute these values into equation 2

θ = cos⁻¹[-27/(6×9)]

θ = cos⁻¹(-27/54)

θ = cos⁻¹(-0.5)

θ = 120°.

Hence the angle between the vector is 120°

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl

1. perpendicular

2. parallel

3. perpendicular