The dot product of a vector with the vectors \(\hat{i}+\hat{j}-3 \hat{k}, \hat{i}+3 \hat{j}-2 \hat{k}\) and \(2 \hat{i}+\hat{j}+4 \hat{k}\) are 0, 5 and 8 respectively. Find the vector.
A. \(\hat{i}+2 \hat{j}+\hat{k}\)
B. \(-\hat{i}+3 \hat{j}-2 \hat{k}\)
C. \(\hat{i}+2 \hat{j}+3 \hat{k}\)
D. \(\hat{i}-3 \hat{j}-3 \hat{k}\)
Answer:A
The dot product of a vector with the vectors \(\hat{i}+\hat{j}-3 \hat{k}, \hat{i}+3 \hat{j}-2 \hat{k}\) and \(2 \hat{i}+\hat{j}+4 \hat{k}\) are 0, 5 and 8 respectively. Find the vector.
A. \(\hat{i}+2 \hat{j}+\hat{k}\) B. \(-\hat{i}+3 \hat{j}-2 \hat{k}\) C. \(\hat{i}+2 \hat{j}+3 \hat{k}\) D. \(\hat{i}-3 \hat{j}-3 \hat{k}\)