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Chapter 10: Q 48. (page 801)

Find a vector in the direction opposite to-4,5,-1 and with magnitude 3.

Short Answer

Expert verified

The required vector is342-4,5,-1.

Step by step solution

01

Step 1. Given information.

The given vector is:

v=-4,5,-1with magnitude 3.

02

Step 2. Find the norm of the vector.

v=-4,5,-1v=-42+52+-12=16+25+1=42

Therefore, the norm of the given vector is 42.

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=-4,5,-1.

The required vector is:

avv=342--4,5,-1=3424,-5,1


Therefore the vector in the direction opposite tov=-4,5,-1and with a magnitude of is 3424,-5,1.

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