Let `vec u` be a vector coplanar with the vectors `vec a = 2 hat i + 3 hat j - hat k` and `vec b= hat j+hatk` If `vec u` is perpendicular to `vec a` and `vec u.vecb=24` then `|vecu|^2` is equal toA. 336B. 315C. 256D. 84

Let `vec u` be a vector coplanar with the vectors `vec a = 2 hat i + 3

1.	Let `vec u` be a vector coplanar with the vectors `vec a = 2 hat i + 3 hat j - hat k` and `vec b= hat j+hatk` If `vec u` is perpendicular to `vec a` and `vec u.vecb=24` then `\|vecu\|^2` is equal toA. 336B. 315C. 256D. 84
Answer» Correct Answer - A If any vector x is coplanar with the vector y and z, then `x=lambday+muz` Here, u is coplanar with a and b. `:." "u=lambdaa+mub` Dot product with a, we get `u.a=lambda(a.a)+mu(b.a)implies0=14lambda+2mu" "…(i)` `[becausea=2hati+3hatj-hatk,b=hatj+hatk,u.a=0]` Dot product with b, we get `u.b=lambda(a.b)+mu(b.b)` `24=2lambda+2mu" "...(ii)[becauseu.b=24]` Solving Eqs. (i) and (ii), we get `lambda=-2,mu=14` Dot product with u, we get `\|u\|^(2)=lambda(u.a)+mu(u.b)` `\|u\|^(2)=-2(0)+14(24)implies\|u\|^(2)=336`

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Let `vec u` be a vector coplanar with the vectors `vec a = 2 hat i + 3 hat j - hat k` and `vec b= hat j+hatk` If `vec u` is perpendicular to `vec a` and `vec u.vecb=24` then `|vecu|^2` is equal toA. 336B. 315C. 256D. 84

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