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Standard XI

Mathematics

Rotation of Axes

Origin is shi...

Question

Origin is shifted to the point P without changing the directions of the axes. If the coordinates of Q with respect to the old axes, new axes are $(2, - 1, 4)$ and $(3, 1, 2)$ respectively, then $P_{x} + P_{y} + P_{z} =$ ?

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Solution

$\begin{matrix} 2 = 3 + h \Rightarrow h = - 1 - 1 + 1 + k \Rightarrow k = - 2 4 = 2 + β \Rightarrow β = 2 P_{x} = - 1 p_{y} = - 2 P_{z} = 2 (h, k, β) \equiv (p_{x}, p_{y}, p_{z}) p_{x} + p_{y} + p_{z} = - 1 \end{matrix}$

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Origin is shifted to the point P without changing the directions of the axes. If the coordinates of Q with respect to the old axes, new axes are (2,−1,4) and (3,1,2) respectively, then Px+Py+Pz=?

2=3+h⇒h=−1−1+1+k⇒k=−24=2+β⇒β=2Px=−1py=−2Pz=2(h,k,β)≡(px,py,pz)px+py+pz=−1

Origin is shifted to the point P without changing the directions of the axes. If the coordinates of Q with respect to the old axes, new axes are $(2, - 1, 4)$ and $(3, 1, 2)$ respectively, then $P_{x} + P_{y} + P_{z} =$ ?

$\begin{matrix} 2 = 3 + h \Rightarrow h = - 1 - 1 + 1 + k \Rightarrow k = - 2 4 = 2 + β \Rightarrow β = 2 P_{x} = - 1 p_{y} = - 2 P_{z} = 2 (h, k, β) \equiv (p_{x}, p_{y}, p_{z}) p_{x} + p_{y} + p_{z} = - 1 \end{matrix}$