Find the resultant of the following vectors. Round to 1 d.p.30∠70°and10∠340°

To find the resultant of the vectors, we first need to convert the polar form vectors to their rectangular form.

The rectangular form of a vector is given by: X = rcos(θ) Y = rsin(θ)

For the first vector 30∠70°: X1 = 30cos(70) = 10.4 (rounded to 1 decimal place) Y1 = 30sin(70) = 28.2 (rounded to 1 decimal place)

For the second vector 10∠340°: X2 = 10cos(340) = 8.1 (rounded to 1 decimal place) Y2 = 10sin(340) = -3.4 (rounded to 1 decimal place)

Now, we add the X and Y components of the vectors to get the resultant vector in rectangular form:

X = X1 + X2 = 10.4 + 8.1 = 18.5 Y = Y1 + Y2 = 28.2 - 3.4 = 24.8

So, the resultant vector in rectangular form is 18.5i + 24.8j.

To convert this back to polar form, we use the following formulas:

r = sqrt(X^2 + Y^2) θ = atan(Y/X)

r = sqrt((18.5)^2 + (24.8)^2) = 30.9 (rounded to 1 decimal place) θ = atan(24.8/18.5) = 53.5° (rounded to 1 decimal place)

So, the resultant of the vectors 30∠70° and 10∠340° is 30.9∠53.5°.