A) 1:1
B) 2:1
C) -1:1
D) 3:1
Correct Answer: A
Solution :
Vector X of the form \[\alpha A+\beta B\] \[X=\alpha A+\beta B\] \[=\alpha (\hat{i}+\hat{j}-2\hat{k})+\beta (\hat{i}-\hat{j}+\hat{k})\] \[X=\hat{i}(\alpha +\beta )+\hat{j}(\alpha -\beta )+\hat{k}(-2\alpha +\beta )\]A vector X is perpendicular to C, ie., \[X-C=0\]\[[\hat{i}(\alpha +\beta )+\hat{j}(\alpha -\beta )]\] \[+\hat{k}(-2\alpha +\beta )].\]\[[2\hat{i}-3\hat{j}+4\hat{k}]=0\] or \[2(\alpha +\beta )-3(\alpha -\beta )+4(-2\alpha +\beta )=0\] or \[2\alpha +2\beta -3\alpha +3\beta -8\alpha +4\beta =0\] or \[-9\alpha +9\beta =0\]or \[\alpha =\beta \] or \[\frac{\alpha }{\beta }=\frac{1}{1}\]or \[\alpha :\beta =1:1\]You need to login to perform this action.
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