If (v-ku) is orthogonal to v, then what is k?? u=[111] and v=[2−12]

Question

If (v-ku) is orthogonal to v, then what is k??  u=[111] and v=[2−12]

wheezym · Accepted Answer

Step 1  We have u=[111] and v=[2−12]   are two column matrices  .  We have to find the value of  k so that (v-ku) is orthogonal to v.  Step 2  First observe that we are given two column matrices u and v. We know that column matrices simply represents a vector in the said space(here R3) .So here u and v are vector in R3.  Now we know that two vectors are orthogonal if their dot product is 0.  Now (v-ku) gives the vector [2−k−1−k2−k] and according to the given problem ,this is orthogonal to  v=[2−12]  So, [2−k−1−k2−k][2−12]=[000]  Since this is simply a vector dot product ,so we can write :  2×(2−k)−1×(−1−k)+2×(2−k)=0  4−2k+1+k+4−2k=0  −3k+9=0  −3k=−9  3k=9  k=3  Which is required value of k and for this value of k (v-ku)  is orthogonal to v.

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

If (v-ku) is orthogonal to v, then what is k?? u=begin{bmatrix}1 11 end{bmatrix} text{ and } v=begin{bmatrix}2 -12 end{bmatrix}

Answered question

Answer & Explanation

New Questions in Precalculus