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Q) A vector 𝑎 ⃗ makes equal angles with all the three axes. If the magnitude of the vector is

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If 𝐚 𝐛 , 𝐜 𝐚𝐧𝐝 𝐝 are four non-zero vectors such that 𝐚 ×𝐛 =𝐜 ×𝐝 and 𝐚 ×𝐜 =𝟒𝐛 ×𝐝

Q) The unit vector perpendicular to the vectors 𝑖 ˆ−𝑗 ˆ and 𝑖 ˆ+𝑗 ˆ is

Q) Let 𝑎 ,𝑏 and 𝑐 be three vectors such that 𝑎 ⋅𝑏 =𝑎 ⋅𝑐 and 𝑎 ×𝑏 =𝑎 ×𝑐 ,𝑎 ≠0. Show