1
Question
Let →a = 2^i ^j + ^k, →b = ^i + 2^j ^k and →c = ^i + ^j 2^k be three vector . A vector in plane of →b and →c , whose projection on →a is a magnitude √2/3 , is
Let →a = 2^i ^j + ^k, →b = ^i + 2^j ^k and →c = ^i + ^j 2^k be three vector . A vector in plane of →b and →c , whose projection on →a is a magnitude √2/3 , is
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Solution
The correct option is B 2^i + 3^j + 3^k
Given,→a=2^ı−^ȷ+^k→b=1+2^ȷ−^k¯c=^ı+^ȷ−2^kA/C vector in the plane of →b and →c is→γ=→b+d(→τ)=^ı+2^ȷ−^k+λ(^ı+^ȷ−2^k)=(1+λ)^ı+(2+λ)^ȷ+(−1−2λ)^k−^ı
Given,projection of →r on →a is √23∴→r⋅→a|→a|=√23⇒∣(1+λ)2−(2+λ)+(−1−2λ)√4+1+1]=√23=∣2+2x−12−λ−1−2A√6∣=√23=1−1−λ1=√2×√3×√2√3=1+λ=2 or −1−λ=2d=1 or λ=−3Onputting the value of λ=1 and -3 we get,→r=2^ı+3^ȷ−3^k and −2^ı−^ȷ+5k
Option B is correct
Given,
→a=2^ı−^ȷ+^k
→b=1+2^ȷ−^k
¯c=^ı+^ȷ−2^k
A/C vector in the plane of →b and →c is
→γ=→b+d(→τ)=^ı+2^ȷ−^k+λ(^ı+^ȷ−2^k)=(1+λ)^ı+(2+λ)^ȷ+(−1−2λ)^k−^ı
Given,
projection of →r on →a is √23
∴→r⋅→a|→a|=√23
⇒∣(1+λ)2−(2+λ)+(−1−2λ)√4+1+1]=√23
=∣2+2x−12−λ−1−2A√6∣=√23
=1−1−λ1=√2×√3×√2√3=1+λ=2 or −1−λ=2d=1 or λ=−3
Onputting the value of λ=1 and -3 we get,
→r=2^ı+3^ȷ−3^k and −2^ı−^ȷ+5k
Option B is correct
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