engineering recuitment BEL Probationary Engineers Mock Test 2025 Mathematics Vector Algebra Scalar and Vector Product
If \({\rm{\vec a}} \times {\rm{\vec b}} = {\rm{\vec c}}\) and \({\rm{\vec b}} \times {\rm{\vec c}} = {\rm{\vec a}}\), then which one of the following is correct?
1
\({\rm{\vec a}},{\rm{\;\vec b}},{\rm{\;\vec c}}\) are orthogonal in pairs and \(\left| {{\rm{\vec a}}} \right| = \left| {{\rm{\vec c}}} \right|\) and \(\left| {{\rm{\vec b}}} \right| = 1\)
2
\({\rm{\vec a}},{\rm{\;\vec b}},{\rm{\;\vec c}}\) are non-orthogonal to each other
3
\({\rm{\vec a}},{\rm{\;\vec b}},{\rm{\;\vec c}}\) are orthogonal in pairs but \(\left| {{\rm{\vec a}}} \right| \ne \left| {{\rm{\vec c}}} \right|\)
4
\({\rm{\vec a}},{\rm{\;\vec b}},{\rm{\;\vec c}}\) are orthogonal in pairs but \(\left| {{\rm{\vec b}}} \right| \ne 1\)