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Vector Calculus
The centroid of a triangle of the triangle OAB is denoted by G. If o is the origin and line(OA) = 4i + 3j, line(OB) = 6i - j,find line(OG) in terms of the unit vectors I and j
a. 10i - 3j
b. 1/2(10i−2j)
c. 10i + 2j
d. 1/3(10i+2j)
a. 10i - 3j
b. 1/2(10i−2j)
c. 10i + 2j
d. 1/3(10i+2j)
Vector Calculus
(a ⃗/a^2 +b ⃗/b^2 )=((a ⃗+b ⃗)/ab)^2
Vector Calculus
Consider the motion of a point P(x(t),y(t)) such that x(t)= cos(t+∅), y= sin(t+∅), t ≥ 0.
a) Show that P moves in a circle
b) If P is initially at (-√3/2, -1/2), find ∅
c) Find the velocity vector of P
d) Show that P has a constant speed of 1
a) Show that P moves in a circle
b) If P is initially at (-√3/2, -1/2), find ∅
c) Find the velocity vector of P
d) Show that P has a constant speed of 1
Vector Calculus
For the Bézier curve x(t)= - t^3 - 2(t)^2 - 1, y(t)= - 2(t)^3 - t + 4, find:
a) the starting point and the finishing point of the curve
b) the left-most and right-most points on the curve
c) the highest and the lowest points on the curve
d) the speed at t = 1/2
a) the starting point and the finishing point of the curve
b) the left-most and right-most points on the curve
c) the highest and the lowest points on the curve
d) the speed at t = 1/2
Vector Calculus
Represent the given velocity 230km/h in the direction 200degree= ___ km
5
4
7
2
5
4
7
2
Vector Calculus
A horizontal force 35N acting to the right,would be indicated by a line -------- and if the chosen vector scale were 1cm = 10N,the line would ______ cm long.
3.5
3
4.5
2
3.5
3
4.5
2
Vector Calculus
Find the dot product of the following vectors
r1=2i+3j−5k,r2=i−2j+4k.Find r1.r2
-24
20
34
23
r1=2i+3j−5k,r2=i−2j+4k.Find r1.r2
-24
20
34
23
Vector Calculus
Solve the following
r1=3i−2j+kr2=2i−4j−3kr3=−i+2j+2kFindr2r3
-16
16
15
-15
r1=3i−2j+kr2=2i−4j−3kr3=−i+2j+2kFindr2r3
-16
16
15
-15
Vector Calculus
Solve the following
r1=3i−2j+kr2=2i−4j−3kr3=−i+2j+2kFindr1r2
7
11
3
10
r1=3i−2j+kr2=2i−4j−3kr3=−i+2j+2kFindr1r2
7
11
3
10
Vector Calculus
Find p such that the vectors w=pi+3j and v=2i + qj are parallel to u=5i + 6j.
2.7
2.5
3.5
4.1
2.7
2.5
3.5
4.1
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