can someone help me with this trig problem Find the dot product of vector v and vector w if:?

Question

v=-5i +6j
W=-2i -3j

Answer 1

v=-5i +6j
W=-2i -3j
now A.B = (mag.A)(mag.B)cos$ where $ is the angle between vector A and B
hence in dot product, i.i = 1,j.j = 1 but i.j = 0 (as cos 0 = 1 and cos 90 = 0)
hence,
v.w = (-5i +6j)(-2i -3j)
= +10i.i + 15i.j - 12j.i - 18j.j
= +10 + 0 - 0 - 18
= 10 - 18
= -8
pls check whether the ans is right or not.

Answer 2

Not sure where Pfo got that definition, but dot product is

-5*-2 + 6*-3 = -8

Answer 3

the simple rule of calculating dot product of 2 vectors is to multiply the similar coefficients & then add them.

here, the x coefficient (coefficient with i) of v & w are 5 & -2. the y coefficients (coeff with j) r 6 & -3. no z coeff (coeff with k).

so , the result is = (5*-2)+(6*-3)= - 28 .

try it with other problems.

Answer 4

The answer is

sqrt((-5)^2 + (-2)^2 + 6^2 + (-3)^2)

-- don't have a calculator handy

Answer 5

v.w = (- 5i + 6j).(- 2i - 3j)
v.w = 10i² + 15i.j - 12 i.j - 18 j²
v.w = - 10 + 3i.j + 18
v.w = 8