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Chapter 10: Q. 13 (page 777)

If the initial point of the vector \(\langle2, 3, 鈭�5\rangle\) is the point \(\left(-3, 2, 4\right)\), what is the terminal point of the vector?

Short Answer

Expert verified

The terminal point of the vector is \(\langle-5,-1,9\rangle\).

Step by step solution

01

Step 1. Given Information

The vector \(v=\langle2,3,-5\rangle\) and the terminal point of the vector is \(\left(-3,2,4\right)\).

02

Step 2. The initial point of vector

If \(v\) is the vector such that \(P\left(x_{0},y_{0},z_{0}\right)\) is the initial point and \(Q\left(x_{1},y_{1},z_{1}\right)\) is the terminal point, then vector \(\overline{PQ}\)is given by \(\overline{PQ}=\langle x_{1}-x_{0},y_{1}-y_{0},z_{1}-z_{0}\rangle\).

Now, the terminal point is (Q\left(-3,2,4\right)\) Let the terminal point be \(P\left(x,y,z\right)\)

Therefore,

\(\langle2,3,-5\rangle=\langle-3-x,2-y,4-z\rangle\)

Comparing both sides,

\(-3-x=2\)

\(2-y=3\)

\(4-z=-5\)

Solve for \(x, y, z\)

\(x=-3-2\)

\(x=-5\)

\(y=2-3\)

\(y=-1\)

\(z=5+4\)

\(z=9\)

Hence, the terminal point of the vector is \(\langle-5,-1,9\rangle\).

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Find PQ鈫�

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