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## All Questions

#### -5 6 1 -3

Volume of parallelopiped,

Here

and,

Given that V is 546, put it in the above equation.

Option (4) is correct

#### Let  is the p.v of the orthocentre and  is the p.v of the centroid of the triangle ABC, where circumcentre is the origin. If  Option 1) 3 Option 2) 2 Option 3) Option 4)

Use the concept of

Position vector -

Let O be a fixed origin, then position vector of P is

- wherein

Centroid is intersection is

orthocentre: intersection of altitudes.

so that in a triangle ABC the orthocentre H, centroid G and circumcentre M are collinear ang G divides HM internally in the ration 2:1

Option 1)

3

Correct option

Option 2)

2

Incorrect option

Option 3)

Incorrect option

Option 4)

Incorrect option

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#### The points with position vectors Option 1) An Equilateral Triangle Option 2) An Isosceles Triangle Option 3) A Right Angle Triangle Option 4) None of these

As we learnt

Scalar Product of two vectors -

- wherein

is the angle between the vectors

So that it is right angle triangle

Option 1)

An Equilateral Triangle

Incorrect option

Option 2)

An Isosceles Triangle

Incorrect option

Option 3)

A Right Angle Triangle

Correct option

Option 4)

None of these

Incorrect option

#### If  Option 1) Positive Option 2) Negative Option 3) Zero Option 4) None

As we learnt

Scalar Product of two vectors -

- wherein

is the angle between the vectors

=  0

Option 1)

Positive

Incorrect Option

Option 2)

Negative

Incorrect Option

Option 3)

Zero

Correct Option

Option 4)

None

Incorrect Option

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#### If vector  and  represents the adjacent sides of any parallelogram then the lenght of diagonal of parallelogram are Option 1) Option 2) Option 3) Option 4) None of these

Magnitude of a Vector -

The length of the directed line segment  is called its magnitude.

- wherein

It is denoted by

Diagonal  = 2i+3j-2k+i+2j+k

Similarly

Option 1)

Incorrect Option

Option 2)

Correct option

Option 3)

Incorrect Option

Option 4)

None of these

Incorrect Option

#### If vector  is perpendicular to   and  is perpendicular to , then Option 1) Option 2) Option 3) Option 4)

Use concept ID

Scalar Product of two vectors -

- wherein

is the angle between the vectors

and

Option 1)

Correct option

Option 2)

Incorrect option

Option 3)

Incorrect option

Option 4)

Incorrect option

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#### If the vector  is collinear with the vector  Option 1) Option 2) Option 3) Option 4) None

Use the concept

Magnitude of a Vector -

The length of the directed line segment  is called its magnitude.

- wherein

It is denoted by

given that

or

Option 1)

Incorrect option

Option 2)

Incorrect option

Option 3)

Correct option

Option 4)

None

Incorrect option

#### If position vectors of A, B, C, D are respectively  and  then Option 1) Option 2) Option 3) A,B,C are collinear Option 4) B,C,D are collinear

As we learnt

Position vector -

Let O be a fixed origin, then position vector of P is

- wherein

Since

So that

Similarly

So that ratios are equal. so they are parellal

Option 1)

Correct option

Option 2)

Incorrect Option

Option 3)

A,B,C are collinear

Incorrect Option

Option 4)

B,C,D are collinear

Incorrect Option

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#### If position vectors of A, B, C, D are respectively  and  then Option 1) Option 2) Option 3)  are collinear Option 4) are collinear

As we learnt

Position vector -

Let O be a fixed origin, then position vector of P is

- wherein

So

So

So

Option 1)

Correct option

Option 2)

Incorrect option

Option 3)

are collinear

Incorrect option

Option 4)

are collinear

Incorrect option

#### Angle between the vectors  Option 1) Option 2) Option 3) Option 4)

As we learnt

Angle between vector a and vector b -

- wherein

Here ??????

Option 1)

Incorrect Option

Option 2)

Incorrect Option

Option 3)

Correct Option

Option 4)

Incorrect Option