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Smooth Curve - Three Dimensional Space
A smooth curve is a curve for which →r' (t) is continuous and →r' (t) ≠ 0 for any t except probably at the endpoints. A helix is a smooth curve, for instance.
At last, there is requirement of discuss integrals of vector functions. By using both limits and derivatives like a guide it shouldn't be too surprising that we as well comprise the following for integration for indefinite integrals
∫ r→ (t) = {∫ f (t)dt, ∫g (t)dt, ∫ h(t) dt} + c→
∫ r→ (t) = ∫ f (t)dt i→ + ∫g (t)dt j→ + ∫ h(t) dt} k→ + c→
and the following for definite integrals.
∫ba r→ (t) dt = {∫ba f (t) dt, ∫ba g (t) dt, ∫ba h(t) dt}
∫ba r→ (t) dt = ∫ba f (t) dt i→ + ∫ba g (t) dt j→ + ∫ba h(t) dt k→
Along with the indefinite integrals we put in a constant of integration to ensure that it was clear that the constant in this case requires being a vector in place of a regular constant.
ABCD is a parallelogram in the given figure, AB is divided at P and CD and Q so that AP:PB=3:2 and CQ:QD=4:1. If PQ meets AC at R, prove that AR= 3/7 AC. Ans: ΔAPR ∼ Δ
use venn diagram to present
Cross Product In this last section we will look at the cross product of two vectors. We must note that the cross product needs both of the vectors to be three dimensional (3D
Properties of Cross product If u, v and w are vectors and c is a number then u → * v → = -v → * w → (cu → ) * v → =
in a garden 1/8 of the flowers are tulips. 1/4 of the tulips are rd. what fraction of the flowers in the garden are red tulips
-cot^2 90^0 + 4 sin 270^0 - 3 tan 180^0
Explain Expressions ? "One set of absolute value signs can only take the absolute value of one number." For example, For the absolute value of negative six plus three,
any example
GCD of "27ab,5xy"
(a) Specify that the sum of the degrees of all vertices of a graph is double the number of edges in the graph. (b) Let G be a non directed gra
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