Answer:The magnitude of (a,b)(a,b)
left parenthesis, a, comma, b, right parenthesis is ∣∣(a,b)∣∣=a2+b2∣∣(a,b)∣∣=a2+b2vertical bar, vertical bar, left parenthesis, a, comma, b, right parenthesis, vertical bar, vertical bar, equals, square root of, a, squared, plus, b, squared, end square root.
WARNING MAY BE TO MUCH!
Step-by-step explanation:The direction angle of (a,b)(a,b)left parenthesis, a, comma, b, right parenthesis is θ=(ba)θ=tan−1(ab)theta, equals, tangent, start superscript, minus, 1, end superscript, left parenthesis, start fraction, b, divided by, a, end fraction, right parenthesis plus a correction based on the quadrant, according to this table:QuadrantHow to adjustQ1(ba)tan−1(ab)tangent, start superscript, minus, 1, end superscript, left parenthesis, start fraction, b, divided by, a, end fraction, right parenthesisQ2(ba)+180°tan−1(ab)+180°tangent, start superscript, minus, 1, end superscript, left parenthesis, start fraction, b, divided by, a, end fraction, right parenthesis, plus, 180, degreeQ3(ba)+180°tan−1(ab)+180°tangent, start superscript, minus, 1, end superscript, left parenthesis, start fraction, b, divided by, a, end fraction, right parenthesis, plus, 180, degreeQ4(ba)+360°tan−1(ab)+360°tangent, start superscript, minus, 1, end superscript, left parenthesis, start fraction, b, divided by, a, end fraction, right parenthesis, plus, 360, degreeVector components from magnitude & directionThe components of a vector with magnitude ∣∣u⃗∣∣∣∣u∣∣vertical bar, vertical bar, u, with, vector, on top, vertical bar, vertical bar and direction θθtheta are (∣∣u⃗∣∣cos(θ),∣∣u⃗∣∣sin(θ))(∣∣u∣∣cos(θ),∣∣u∣∣sin(θ))left parenthesis, vertical bar, vertical bar, u, with, vector, on top, vertical bar, vertical bar, cosine, left parenthesis, theta, right parenthesis, comma, vertical bar, vertical bar, u, with, vector, on top, vertical bar, vertical bar, sine, left parenthesis, theta, right parenthesis, right parenthesis.What are vector magnitude and direction?We are used to describing vectors in component form. For example, (3,4)(3,4)left parenthesis, 3, comma, 4, right parenthesis. We can plot vectors in the coordinate plane by drawing a directed line segment from the origin to the point that corresponds to the vector's components:yyxx(a,b)(a,b)Considered graphically, there's another way to uniquely describe vectors — their magnitudemagnitudestart color #11accd, start text, m, a, g, n, i, t, u, d, e, end text, end color #11accd and directiondirectionstart color #1fab54, start text, d, i, r, e, c, t, i, o, n, end text, end color #1fab54:yyxx(a,b)(a,b)∣∣u⃗∣∣∣∣u∣∣θθThe magnitudemagnitudestart color #11accd, start text, m, a, g, n, i, t, u, d, e, end text, end color #11accd of a vector gives the length of the line segment, while the directiondirectionstart color #1fab54, start text, d, i, r, e, c, t, i, o, n, end text, end color #1fab54 gives the angle the line forms with the positive xxx-axis.The magnitude of vector v⃗vv, with, vector, on top is usually written as ∣∣v⃗∣∣∣∣v∣∣vertical bar, vertical bar, v, with, vector, on top, vertical bar, vertical bar. Sorry For all this I hope it helped :[