InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Given two orthogonal vectors `vecA and VecB` each of length unity. Let `vecP` be the vector satisfying the equation `vecP xxvecB=vecA-vecP`. then which of the following statements is false ?A. vectors `vecP, vecA and vecP xx vecB` ar linearly dependent.B. vectors `vecP, vecB and vecP xx vecB` ar linearly independentC. `vecP` is orthogonal to `vecB` and has length `1/sqrt2`.D. none of these |
|
Answer» Correct Answer - d `vecPxxvecB=vecA-vecP and |vecA|=|vecB|=1 and vecA.vecB=0`is given Now `vecP xx vecB = vecA-vecP` `(vecPxxvecB) xxvecB= (vecA-vecP)xxvecB` (taking cross product with `vecB` on both sides) `or (vecP.vecB)vecB- (vecB.vec B)vecP=vecAxxvec B -vecP xx vecB` `or (vecP.vecB) vecB-vecP=vecA xx vecB-vecA+vecP` `or 2vecP = vecA-vecA-vecAxxvec B-(vecP.vecB)vecB` `or vecP= (vecA-vecAxxvecB=-(vecP.vecB)vecB)/2` taking dot product with `vecB` on both sides of (i) get `vecP.vecB=vecA.vecB-vecP.vecB`ltbr gt `Rightarrow vecP.vecB=0` `Rightarrow vecP=( vecA + vecBxxvecA)/2` Now `(vecP xx vecB) xx vecB= (vecP.vecB) vecB-(vecB.vecB) vecP=-vecP` `vecP,vecA,vecPxxvecB(=vecA-vecP)` are depenment Also `vecP.vecB=0` ` and |vecP|^(2)=|(vecA-vecAxxvecB)/2|^(2)` `(|vecA|^(2)+|vecAxxvecB|^(2))/4` `(1+1)/4=1/2or |vecP|=1/sqrt2` |
|