1.1.1 Show how to find A and B, given A+B and A −B.
1.1.2 The vector A whose magnitude is 1.732 units makes equal angles with the coordinate axes. Find Ax,Ay , and Az. 1.1.3 Calculate the components of a unit vector that lies in the xy-plane and makes equal angles with the positive directions of the x- and y-axes. 1.1.4 The velocity of sailboat A relative to sailboat B, vrel, is defined by the equation vrel = vA − vB, where vA is the velocity of A and vB is the velocity of B. Determine the velocity of A relative to B if vA = 30 km/hr east

vB = 40 km/hr north.
ANS. vrel = 50 km/hr, 53.1◦ south of east.
1.1.5 A sailboat sails for 1 hr at 4 km/hr (relative to the water) on a steady compass heading of 40◦ east of north. The sailboat is simultaneously carried along by a current. At the end of the hour the boat is 6.12 km from its starting point. The line from its starting point to its location lies 60◦ east of north. Find the x (easterly) and y (northerly) components of the water’s velocity. ANS. veast = 2.73 km/hr, vnorth ≈ 0 km/hr.

1.1.6 A vector equation can be reduced to the form A = B. From this show that the one vector equation is equivalent to three scalar equations. Assuming the validity of Newton’s second law, F = ma, as a vector equation, this means that ax depends only on Fx and is independent of Fy and Fz. 1.1.7 The vertices A,B, and C of a triangle are given by the points (−1, 0, 2), (0, 1, 0), and (1,−1, 0), respectively. Find point D so that the figure ABCD forms a plane parallelogram. ANS. (0,−2, 2) or (2, 0,−2). 1.1.8 A triangle is defined by the vertices of three vectors A,B and C that extend from the origin. In terms of A,B, and C show that the vector sum of the successive sides of the triangle (AB +BC +CA) is zero, where the side AB is from A to B, etc. 1.1.9 A sphere of radius a is centered at a point r1. (a) Write out the algebraic equation for the sphere.

(b) Write out a vector equation for the sphere.
ANS. (a) (x −x1)2 +(y −y1)2 + (z...

...each of the following vectors in terms of and
(a)
(b)
(c)
(Total 4 marks)
2. The vectors , are unit vectors along the x-axis and y-axis respectively.
The vectors = – + and = 3 + 5 are given.
(a) Find + 2 in terms of and .
A vector has the same direction as + 2 , and has a magnitude of 26.
(b) Find in terms of and .
(Total 4 marks)
3. The circle shown has centre O and radius 6....

...December 2011
Vectors
Math is everywhere. No matter which way you look at it, it’s there. It is especially present in science. Most people don’t notice it, they have to look closer to find out what it is really made of. A component in math that is very prominent in science is the vector. What is a vector? A vector is a geometric object that has both a magnitude and a direction. A good example of a vector is wind. 30 MPH...

...VectorAnalysis
Definition
A vector in n dimension is any set of n-components that
transforms in the same manner as a displacement when you
change coordinates
Displacement is the model for the behavior of all vectors
Roughly speaking: A vector is a quantity with both direction as well as
magnitude.
On the contrary, a scalar has no direction and remains unchanged when
one changes the coordinates.
Notation: Bold...

...Sciences
ECE / ICE / MexE Department
ECE 352 VECTORANALYSIS
DEL OPERATOR
GROUP 3 Andaya, Rizalyn Ramos, Maria Issa P.
∇
Del is a symbol used in mathematics, in particular, in vector calculus, as a vector differential operator, usually represented by the nabla symbol ∇. Del may denote the gradient (locally steepest slope), the divergence of a vector field, or the curl (rotation) of a vector...

...Research paper about vector organisms such as ticks and mosquitoes and ways to remove them.
Vector Organisms and the Diseases They Carry
Vector organisms are parasites that transmit various diseases. Two vector organisms are ticks and mosquitoes. These two vector organisms transmit many well-known diseases. Through most of this essay, I will be explaining these two different organisms and the diseases that they carry....

...disease. The company offers customers support services. It markets its products worldwide. Immunetics is headquartered in Boston, Massachusetts, the US.
To Read Complete Report with TOC: http://www.marketresearchreports.biz/analysis/225566
This report is a source for data, analysis, and actionable intelligence on the companys portfolio of pipeline products. The report provides key information about the company, its major products and brands.
The report...

...is acting is referred to as a vector. It is not enough to know that a thousand pounds of force is being exerted on a person. A thousand pounds of force can crush the person into the earth or send the person flying into the air, depending on the vector. Vector mathematics can be used to calculate the resultant effect when more than 1 vector is acting on an object. Vector mathematics also can be used to take the recorded...