Given below are two statements. STATEMENT - 1: a b =(( i a ) b ) i +(( j a ) b ) j +(( k…
Mathematics · JEE Main · NTA Exams — Vector Algebra
STATEMENT - 1: \(\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}}=((\hat{\hat{i}} \times \overrightarrow{\mathbf{a}}) \cdot \overrightarrow{\mathbf{b}}) \hat{i}+((\hat{\hat{j}} \times \overrightarrow{\mathbf{a}}) \cdot \overrightarrow{\mathbf{b}}) \hat{j}+((\hat{\mathbf{k}} \times \overrightarrow{\mathbf{a}}) \cdot \overrightarrow{\mathbf{b}}) \hat{\mathbf{k}}\)
STATEMENT - 2: \(\vec{c}=(\hat{i} \cdot \vec{c}) \hat{i}+(\hat{j} \cdot \vec{c}) \hat{j}+(\hat{k} \cdot \vec{c}) \hat{k}\).
In the light of the above statements, choose the correct answer from the options given below:
- Both the statements are true and Statement - 2 is the correct explanation for Statement - 1
- Both the statements are true but Statement - 2 is not the correct explanation for Statement - 1
- Statement - 1 is true and Statement - 2 is false
- Statement - 1 is false and Statement - 2 is true
Answer
(A) Both the statements are true and Statement - 2 is the correct explanation for Statement - 1
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