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qUESTIONS

Given ā = î + 2ĵ and b̅ = 2î + ĵ, what are the magnitudes of the two vectors? Are these two vectors equal?

Find a unit vector in the direction of the vector 3î+ 4ĵ

Water is flowing in a stream with velocity 5 km/hr in an easterly direction relative to the shore. Speed of a boat is relative to still water is 20 km/hr. If the boat enters the stream heading North, with what velocity will the boat actually travel?

From the following figure, determine the resultant of four forces

Express vector AC in terms of vectors AB and CB shown in the following figure.

The length, breadth and thickness of a rectangular sheet of metal are 4.234 m, 1.005 m, and 2.01 cm respectively. Give the area and volume of the sheet to correct significant figures and is initial velocity.

v= at + b/(t+c) + v0 is a dimensionally valid equation. Obtain the dimensional formula for a, b and c where v is velocity, t is time and v0

The diameter of a sphere is 2.14 cm. Calculate the volume of the sphere to the correct number of significant figures.

Write down the number of significant figures in the following: 0.003 m^2 , 0.1250 gm cm^-2, 6.4 x 10^6 m, 1.6 x 10^-19 C, 9.1 x 10^-31 kg.

If the formula for a physical quantity is X= (a^4x b^3)/(c^(1/3)d^(1/2)) and if the percentage error in the measurements of a, b, c and d are 2%, 3%, 3% and 4% respectively. Calculate percentage error in X.

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