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Chapter 9: Q. 17 (page 612)

Find a so that the vectors v=i-aj and w=2i+3j are orthogonal.

Short Answer

Expert verified

The value ofais23.

Step by step solution

01

Step 1. Concept Used

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

02

Step 2. Find the dot product

For the vectors v=i-ajand w=2i+3jthe dot product is given as

v路w=(i-aj)路(2i+3j)v路w=1路2+(-a)路3v路w=2-3a

03

Step 3. Form the equation and solve for a

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

v路w=02-3a=0

On solving the equation we get

2-3a-2=0-2-3a=-2-3a-3=-2-3a=23

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