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#### Let the volume of a parallelopiped whose coterminous edges are given by and be 1 cu. unit. If be the angle between the edges and then can be : Option: 1 Option: 2 Option: 3 Option: 4 Dot (Scalar) Product in Terms of Components -

Angle between two vectors -

Geometrical Interpretation of Scalar Triple Product -

Let vectors and represented the sides of a parallelepiped OA, OB and OC respectively. Then, is a vector perpendicular to the plane of and . Let ? be the angle between vectors and and α be the angle between and .

If is a unit vector along , then α is the angle between and .  - Correct Option (3)

#### Let and be two vectors. If is a vector such that and then is equal to : Option: 1 Option: 2 Option: 3 Option: 4 Vector Triple Product -

For three  vectors and vector triple product is defined as . - Correct Option (3)

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• Faculty Support #### Let and be three unit vectors such that .If and then the ordered pair, is equal to : Option: 1 Option:2 Option: 3 Option: 4 Addition and subtraction of Vectors -

The sum of two vectors is always a vector. Properties of vector Subtraction -   Correct Option (3)

#### Let be three mutually perpendicular vectors of the same magnitude and equally inclined at an angle , with the vector . Then is equal to ________.

Given,

and these are mutually perpendicular,

So,

Angle of with

Now,

Using this in (i)

Hence, the correct answer is 4

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• Faculty Support #### Let . Let a vector be in the plane containing . If is perpendicular to the vector and its projection on is 19 units, then is equal to___________

(a vector in the plane of & and perpendicular  to )

#### Let be three vectors mutually perpendicular to each other and have same magnitude. If a vector satisfies then is equal to :Option: 1 Option: 2 Option: 3 Option: 4 Give expression is

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option (4)

#### The angle between the straight lines, whose direction cosines are given by the equations , is :Option: 1 Option: 2 Option: 3 Option: 4 ...............(1)

..........(2)

From (1) and (2)

So

Also

So

Angle

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• Faculty Support #### If the projection of the vector on the sum of the two vectors and is 1, then is equal to ________.

Sum of vectors (  ) is

Projection of on is  