If a = 2î + ĵ + 2k̂, then the value of |î × (a × î)|² + |ĵ × (a × ĵ)|² + |k̂ × (a × k̂)|² is equal to
If a = 2î + ĵ + 2k̂, then the value of |î × (a × î)|² + |ĵ × (a × ĵ)|² + |k̂ × (a × k̂)|² is equal to
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1 Answer
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Let a? = xî + y? + zk
î × (a? × î) = (î·î)a? – (a? ·î)î = y? + zk
Similarly? × (a? ×? ) = xî + zk and k? × (a? × k? ) = xî + yk
|î × (a? × î)|² + |? × (a? ×? )|² + |k? × (a? × k? )|²
= |y? + zk|² + |xî + zk|² + |xî + y? |² = 2|a? |² = 2 (9) = 18
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