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Motion In A Plane

Question
CBSEENPH11018281
Wired Faculty App

What is the geometric meaning of dot product?

Solution

The dot product of two vectors is given by, 
            straight A with rightwards arrow on top times straight B with rightwards arrow on top space equals space AB space cosθ space equals space straight A left parenthesis straight B space cosθ right parenthesis 
Dot product is a scalar quantity. 

Bcosstraight theta is the magnitude of component straight B with rightwards harpoon with barb upwards on top in the direction of A with rightwards harpoon with barb upwards on top 
straight A with rightwards harpoon with barb upwards on top. B with rightwards harpoon with barb upwards on top space equals space left parenthesis M a g n i t u d e space o f space v e c t o r space A with rightwards harpoon with barb upwards on top right parenthesis space left parenthesis m a g n i t u d e space o f space c o m p o n e n t space o f space B with rightwards harpoon with barb upwards on top space i n space t h e space d i r e c t i o n space o f space A with rightwards harpoon with barb upwards on top space right parenthesis
Similarly, 
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       = (Magnitude of vector straight B with rightwards harpoon with barb upwards on top) (magnitude of component of straight A with rightwards harpoon with barb upwards on top in the direction of straight B with rightwards harpoon with barb upwards on top space right parenthesis
)

Some More Questions From Motion in A Plane Chapter

What is a vector quantity?

Give three examples of scalar quantities.

Give three examples of vector quantities.

What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

Is a physical quantity, having a direction, necessarily a vector?

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

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