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Vectors Quetiones

  • #1

Homework Statement


1. How can i determine the angle between two vectors
2. The Component of vector ( a vector, given below ) along the direction of i+j
3. Let there be a vector and b vector , then find component the component of a vector along perpendicular direction of b vector.

Please also do tell me what do you mean by along the direction and perpendicular to some vector and projection.


Homework Equations


a vector=2i + 3j + 4k
b vector = 3i + 4j + 5k


The Attempt at a Solution


Not Attempted yet cuz didn't understand it's meaning.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
rl.bhat
Homework Helper
4,433
5
Search the relevant equations for dot product and cross product of the vectors, projection of one vector on the other vector from any text book or web site.
 
  • #3
53
0
Perpendicular (orthogonal) means that the vectors are at a 90 degree angle or pi/2 radians with each other.

Along, would mean they are parallel (angle between = 0)

As for the formulas:

A "dot" B = |A|*|B|*sin(angle between them) = AxBx + AyBy + AzBz

A "cross" B = A x B = |A|*|B|*sin(angle between them) = det( [i,j,k ; Ax,Ay,Az ; Bx,By Bz] )
 
  • #4
Perpendicular (orthogonal) means that the vectors are at a 90 degree angle or pi/2 radians with each other.

Along, would mean they are parallel (angle between = 0)

As for the formulas:

A "dot" B = |A|*|B|*sin(angle between them) = AxBx + AyBy + AzBz

A "cross" B = A x B = |A|*|B|*sin(angle between them) = det( [i,j,k ; Ax,Ay,Az ; Bx,By Bz] )
My physics teacher told me the formula is : A "dot" B = |A|*|B|*cos(angle between them) ( not sin )
 
  • #5
rl.bhat
Homework Helper
4,433
5
My physics teacher told me the formula is : A "dot" B = |A|*|B|*cos(angle between them) ( not sin )
It is right. Since you know this formula why can't you find the angle between the vectors?
 
  • #6
i founded it.
but i can't get what it means by " Find The component of Avec along the direction of i+j "
 
  • #7
53
0
My physics teacher told me the formula is : A "dot" B = |A|*|B|*cos(angle between them) ( not sin )
Oops, I remember changing that mistake, but yeah it is cosine.

A projection along i+j is the dot product of

Vector1 and Unit vector of i+j, it is the component of vector1 along the vector i+j.
 

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