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Chapter 10: Q 51. (page 801)

Find a vector of length 3 that points in the direction opposite to1,-2,3.

Short Answer

Expert verified

The required vector is314-1,2,-3.

Step by step solution

01

Step 1. Given information.

The given vector is:

v=1,-2,3 and its length is 3.

02

Step 2. Find the norm of the vector.

v=1,-2,31v=12+-22+32=1+4+9=14

Therefore, the norm of the given vector is 14.

03

Step 3. Find the vector.

We know that the vector in the direction of vis av-v. Here ais the magnitude of the given vector and the negative sign shows the direction opposite tov=1,-2,3.

The required vector is:

avv=314-1,-2,3=314-1,2,-3


Therefore the vector in the direction opposite to v=1,-2,3is314-1,2,-3.

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