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Chapter 9: Q. 18 (page 612)

Find b so that the vectors v=i+j and w=i+bj are orthogonal.

Short Answer

Expert verified

The value ofbis-1.

Step by step solution

01

Step 1. Concept Used 

When two vectors uand vare orthogonal then their dot product is zero that is u路v=0.

02

Step 2. Find the dot product 

For the vectors v=i+jand w=i+bjthe dot product is given as

v路w=(i+j)路(i+bj)v路w=1路1+1路bv路w=1+b

03

Step 3. Form the equation and solve for b

As the vectors vand ware orthogonal so their dot product is zero and so the equation is formed as

v路w=01+b=0

On solving the equation we get

1+b-1=0-1b=-1

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