Project ForgeEngineering Mathematics
Linear Algebra
GATE 2022
Medium
Consider two vectors: a = 5i + 7j + 2k, b = 3i − j + 6k. Magnitude of the component of a orthogonal to b in the plane containing the vectors a and b is ___________ (round off to 2 decimal places).
8.32(± 0.05 accepted)
Explanation
a·b = 15-7+12 = 20. |b|² = 9+1+36 = 46. |a|² = 25+49+4 = 78. Since the parallel and orthogonal components of a (relative to b) are perpendicular, |a_orth|² = |a|² − (a·b)²/|b|² = 78 − 400/46 = 78 − 8.6957 = 69.3043. |a_orth| = √69.3043 ≈ 8.32.
Source: GATE ME 2022 Session 1 (ME-1) (2022)
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