Projection of Vector on a line or direction MCQ Quiz in मराठी - Objective Question with Answer for Projection of Vector on a line or direction - मोफत PDF डाउनलोड करा

Explanation:

The additive inverse vector of vector pi + 2j - 3k is

-pi - 2j + 3k

So,  = -pi - 2j + 3k

Comparing both sides

So, p = 9, b = 4

Putting in  we get

i.e., 4b = 91

i.e., b = 81/4

Hence p = 9, b = 4, a = 81/4

Option (2) is true.

Vector perpendicular to plane containing the vectors and is parallel to vector

Required magnitude of projection

Concept Used:

Projection of vector on is

Calculation

Given:

, , 

Projection of AB on AC =

Projection of AB on AC =

Hence option 2 is correct

Answer : 3

Solution :

Vector projection of  on  

=  

=  

= 

Concept:

Let  be two vectors. Then the vector component of the vector  is given by:

Calculation:

Given:

 and 

|| = √52 

The component of vector a along b is 

Mistake PointsWe are asked to find the vector component of 'a' along 'b'. If the scalar component was asked, then there would have been only 5 in the denominator.

Explanation:

The projection vector of  on  is given by .

The correct answer is option 2.

Concept:

The projection of vector   on  is given by .

Calculation:

Given   = 2î − ĵ + k̂  and   = î + 2ĵ + 2k̂

  = ( 2î − ĵ + k̂ )⋅ ( î + 2ĵ + 2k̂ )

= 2 × 1 + (-1) × 2 + 1 × 2 

= 2 - 2 + 2

= 2

|| = | î + 2ĵ + 2k̂ |

= 

=  

= 3

The projection of vector   on   = \(\frac{\rm\vec{a}⋅\rm\vec{b}}{|\vec b|}\).

= 

The projection of vector  = 2î − ĵ + k̂ along  = î + 2ĵ + 2k̂ is 2/3.

The correct answer is option 1.

Concept -

Use of normal vector  and projection vector

projection of  on  is 

Solution - 

Normal vector to the plane to plane containing  and  is 

Projection of  on  = 

= 

Hence the final answer is option 2.