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Chapter 10 Vector Algebra Ex 10.3 Solutions

Question - 1 : - Find the angle between two vectors and with magnitudes √3 and 2, respectively having .

Answer - 1 : -

Firstly let us consider,

Question - 2 : - Find the angle between the vectors

Answer - 2 : -

Let us consider the

Hence, the angle between the vectors is cos-1 (5/7).

Question - 3 : -

Find the projectionof the vectoron the vector.

Answer - 3 : -

Firstly,

Question - 4 : - Find the projection of the vector  on the vector  .

Answer - 4 : -

Firstly,

Hence, the projection is 60/√114.

Question - 5 : -
Show that each of the given three vectors is a unit vector:
 
Also, show that they are mutually perpendicular to each other.

Answer - 5 : -

It is given that

Question - 6 : - Find

Answer - 6 : -

Let us consider,

Question - 7 : - Evaluate the product

Answer - 7 : -

Let us consider the given expression,

Question - 8 : - Find the magnitude of two vectors  , having the same magnitude and such that the angle between them is 60° and their scalar product is ½.

Answer - 8 : -

Firstly,

Hence the magnitude of two vectors is 1.

Question - 9 : -

Answer - 9 : -

Let us consider,

Hence the value is √13.

Question - 10 : - If are such that  is perpendicular to , then find the value of λ.

Answer - 10 : -

We know that the

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