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Vector Calculus
An airplane flies at 400 miles per hour due east in a wind blowing at 50 miles per hour
from southeast. What is the flying speed and direction of the plane relative to the ground?
from southeast. What is the flying speed and direction of the plane relative to the ground?
Vector Calculus
Given vector u = (-1, 1, 2) and vector v = (0, 1, 0).
a) u x v , and
b) Show that u x v is orthogonal to both u and v.
a) u x v , and
b) Show that u x v is orthogonal to both u and v.
Vector Calculus
Given vector u = (0, 3, 3) and vector v = (-1, 1, 1).
a) Find the projection of u onto v, and
b) Find the vector component of u orthogonal to v.
[Give your answers in the form of linear combination of the standard unit vectors (i , j , and k ) ]
a) Find the projection of u onto v, and
b) Find the vector component of u orthogonal to v.
[Give your answers in the form of linear combination of the standard unit vectors (i , j , and k ) ]
Vector Calculus
why field lines stops and start at infinity?
Vector Calculus
Jetty a on the mainland and jety B on a resort island are 36km apart.The bearing of jetty B is 060 degree celcius from jetty A. A ferry, with an average speed of 10 meter per secondin still water, travels between jetty A and jetty B.
1. a) Suppose that the current flows from west to east with a speed of v meter per second, where v<10.Using a vector method, show that the course on which the ferry must be steered in order to travel from jetty A to B is θ degree celcius east of north, where θ=60 degree celcius-inverse sin(v/20)
1. a) Suppose that the current flows from west to east with a speed of v meter per second, where v<10.Using a vector method, show that the course on which the ferry must be steered in order to travel from jetty A to B is θ degree celcius east of north, where θ=60 degree celcius-inverse sin(v/20)
Vector Calculus
if a and b are perpendicular then prove that [a2+b2]=[a]2+[b]2
Vector Calculus
if a+b+c=0, |a|=3, |b|=5 and |c|=7, then find the angle between a and b.
Vector Calculus
Find the cosines of the angles that the line r = [-3,2,5] + t[2,2√2] makes with the coordinate axes
Vector Calculus
if magnitiude of three vectors ,what will be the direction between them so that the resultant will be zero?
Vector Calculus
Find the equation of the plane which contain the line of intersection of the planes vector r.(i+2j+3k)-4=0 and vector r.(2i+j-k)+5=0 and which is perpendicular to the plane vector r.(5i+3j-6k)-8=o.
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