The sketch below show Cartesian coordinates converted to polar coordinates. P(x,v) P(r,0) P(r,e) The question now arise can we find polar unit vectors, f and Ô which describe the direction along ř'and 0 of increasing r if 0 held constant and 0 if r is held constant ?, as shown in the above sketch. The answer is yes. The polar unit vectors are given by the following mathematical dy formula in the Cartesian coordinate system, f =i+2 j and 0 Or 1.1 Use the above formula to determine expressions for the polar unit vectors î and ô. i+ dr j and ô =- j to 3-dimesional 1.2 Extend this the 2-dimesional formula formula and use it to determine expressions for the spherical unit vectors of (f, ê, »). 1.3 Express the position vector, = 3i +4}+ 5k in cylindrical coordinates (r, 0,z). Before doing the conversion first conceptualise the position vector, 7 3i +4j + 5k. Clearly indicate r and 0 on the sketch.

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.