Angle Between Two Vectors & Components Calculation

[dhruv_arora]

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 because didn't understand it's meaning.

 

[rl.bhat]

Search the relevant equations for dot product and cross product of the vectors, projection of one vector on the other vector from any textbook or web site.

 

[iamthegelo]

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] )

 

[dhruv_arora]

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 )

 

[rl.bhat]

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?

 

[dhruv_arora]

i founded it.
but i can't get what it means by " Find The component of Avec along the direction of i+j "

 

[iamthegelo]

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.