Vector Algebra

⭐ Important Questions

1. Find projection of a on b if a = i + 2j + k and b = 2i - j + 2k.
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   a·b = 1(2) + 2(-1) + 1(2) = 2 - 2 + 2 = 2\n|b| = √4+1+4 = 3\nProjection = a·b|b| = 2/3
2. Find area of parallelogram with adjacent sides a=i+2j+3k and b=3i+2j+k.
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   a x b = |i j k; 1 2 3; 3 2 1|\n= i(2-6) - j(1-9) + k(2-6)\n= -4i + 8j - 4k\nArea = |a x b| = √16+64+16 = √96 = 4√6