Practicing Success
It is given that $\vec{t_1}=2\hat i-\hat j+\hat k$ and $\vec{t_2}=\hat i+3\hat j-2\hat k$, $\vec{t_3}=-2\hat i+\hat j-3\hat k$ and $\vec{t_4}=3\hat i+2\hat j-5\hat k$. If $\vec{t_4}=p$ $\vec{t_1}+q\vec{t_2}+r\vec{t_3}$, then |
p = qr p = q + r p = q = r $q=\frac{2pr}{p+r}$ |
p = q + r |
We have $3\hat i+2\hat j-5\hat k= p(2\hat i-\hat j+\hat k) + q(\hat i+3\hat j-2\hat k) + r(-2\hat i+\hat j-3\hat k)$ ⇒ 2p + q – 2r = 3, …….. (1) – p + 3q +r =2, p – 2q – 3r = –5. Adding all the equations, we get 2p +2q = 4r i.e. p + q = 2r. Equation (1) gives p = 3 ⇒ q = 1, r = 2. With these values of q, p, r, only (B) is the correct answer. |