Given Vector A: 15cm at zero degrees and Vector B: 30cm at 60 degrees, How do you add and subtract these two vectors?

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Answer 1 · 2017-01-16T04:36:44

$vecA + vec B$ is $15sqrt7$ cm long, at $40.89^o$ and
$vec B-vec A$ is $15sqrt3$ cm long, at $90^o$ .

The vector with modulus ( length ) r, and in the direction inclined at

$theta^o$ to x-axis in the anticlockwise ( + ) sense, has

#(r, theta)

$as the polar$ (|..|, angle)# form,

but component-wise, it is

$r < cos theta, sin theta > = < x, y >$ .

Here,

$vec A= (15, 0^o) = 15 <cos 0^o,5 sin 0^0 >=15<1, 0>$ and

$vec B= (30, 60^o) = < 30 cos 60^o, 30 sin 60^o >$

$=<15, 15sqrt3>=15 <1, sqrt3>$ .

Now, with component-wise addition and subtraction,

$vecA + vec B = 15<1, 0>+15<1, sqrt3>=15<2, sqrt3>$ and

$vec B - vec A =15<1, sqrt3> -15<1, 0> = 15<0, sqrt3>$

The polar $(|..|, angle)$ forms are

$vec A + vec B =( 15sqrt7, 40.89^o)$ , nearly, and

$vec B - vec A= (15sqrt3, 90^o)$ .