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Vector Calculus
If A=2i+j+k, B=i-2j+2k, and C=3i-4j+2k, find the projection of A+C in the direction of B.
Vector Calculus
Find a unit vector in the direction of the resultant of vectors A=2i-j+k, B=i+j+2k, C=3i-2j+4k.
Vector Calculus
Suppose the sides of a closed polygam represent vector arrangend head to tail rule , what is sum of these vectors ?
Vector Calculus
Show that the sum and difference of two perpendicular vectors of equal lengths are also perpendicular and of some lengths ?
Vector Calculus
Two workers are pulling on ropes attached to a tree stump one of them pull by 50 N and another one pull by 40 N the angle between tow forces is 60 degree . Find the magnitude and direction of the resultant force on the tree.
Vector Calculus
the straight line l has equation r=i+6j-3k+s(i-2j+2k). the plane p has equation (r-3i).(2i-3j+6k)=0. the line l intersects the plane p at the point A. Find a vector equation for the line which lies in p, passes through A and is perpendicular to l ?
Vector Calculus
let u+v+w=0 and ||U||=3, ||v||=5, and ||w||=7, then show that the angle between u and v is pie/3?
Vector Calculus
Let T:R =R be defined by T(x,y)=(x+y,x) show that T is a linear Transformation
Vector Calculus
Suppose that {v1.....Vn} is a basis for the vector space V. Given any vector v element of V, we can express v as a linear combination v = X1V1+.....+XnVn. The uniqueness of this expression means that mapping v to the n-tuple of coefficients (X1...Xn) defines a function O: V - R^n. Prove that this function is a bijection.
Vector Calculus
Given three points A=(2, -3, 4), B=(0, 1, 2), and C=(-1, 2, 0) in a 3-D coordinate systems. Find the area of the triangle with A, B, and C as vertices.
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