The vectors u=mxvector i+2xvector j, vector v=3xvector i-vector j are perpendicular . what is m?
1 Answer | Add Yours
The problem provides the information that the vectors are orthogonal, hence, evaluating its dot product yields 0.
`bar u*bar v = 0`
You need to perform the multiplication of the vectors `bar u` and `bar v` , such that:
`(m*bar i + 2*bar j)(3*bar i - bar j) = 0`
`m*bar^2 i - m*bar i*bar j + 6*bar i*bar j - 2bar^2 j = 0`
Since `bar i*bar j = 0` and `bar^2 i = bar^2 j = 1` yields:
`m - 2 = 0 => m = 2`
Hence, evaluating m, using the information that `bar u` is perpendicular to `bar v` , yields `m = 2.`
Join to answer this question
Join a community of thousands of dedicated teachers and students.Join eNotes