AP EAMCET · Maths · Vector Algebra
If \(\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{c}=4 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+7 \hat{\mathbf{k}}\), then the vector \(r\) satisfying \(r \times b=c \times b\) and \(r . a=0\) is
- A \(\hat{\mathbf{i}}+8 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}\)
- B \(\hat{\mathbf{i}}-8 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}\)
- C \(\hat{\mathbf{i}}-8 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}\)
- D \(\hat{\mathbf{-i}}-8 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}\)
Answer & Solution
Correct Answer
(D) \(\hat{\mathbf{-i}}-8 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}\)
Step-by-step Solution
Detailed explanation
(d) Three vectors \(\mathrm{a}, \mathrm{b}\) and \(\mathrm{c}\) are given as, \(a=2 \hat{i}+\hat{k}, b=\hat{i}+\hat{j}+\hat{k}\) and \(c=4 \hat{i}-3 \hat{j}+7 \hat{k}\) Given condition, \(\mathrm{r} \times \mathrm{b}=\mathrm{c} \times \mathrm{b}\)…
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