Vectors Quetiones

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.

The Attempt at a Solution

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rl.bhat
Homework Helper
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.

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] )

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
Homework Helper
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?

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

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.