Finding Prependicular Unit Vectors in 3D Space

[brad sue]

Hi please, someone help me with those problems?

It's about three dimension space and it is about vectors properties:

Find the unit vectors u that are prependicular to both i+2j+k and 3i-4j+2k.

the second is:

Find two mutually perpendicular unit vectors that are perpendicular to 2i+3j

Thank you for your help

Brad

 

[da_willem]

Express the vector(s) you seek in terms of unknown coefficients (e.g. ai+bj+ck) and use the definition of 'perpendicular' (i.e. the dotproduct is zero) to find equations you can solve for these unknowns.

 

[TD]

You can also use the fact that the outer product (vectorial) of two vectors gives a new vector which is perpendicular to the first two. Divide by the norm to make it a unit vector.

 

[brad sue]

thanks

OK I going to try your suggestion

Express the vector(s) you seek in terms of unknown coefficients (e.g. ai+bj+ck) and use the definition of 'perpendicular' (i.e. the dotproduct is zero) to find equations you can solve for these unknowns.

 

[mathmike]

a vector perpendicular to two separate vectors is created by using the cross product