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Consider the position vectori=1,0,0in 3Describe the set of position vectors vin $3with the property thatv·i=0.

Short Answer

Expert verified

The position vector should lie onyz-plane so thatv·i=0holds.

Step by step solution

01

Step 1:Given information

i=1,0,0in3

02

Step 2:Explaination

Consider the position vectori=1,0,0in3

Assume that the vector vin3has the position vectorv=a,b,c.

The dot product ofv=a,b,candi=1,0,0is0.

Therefore

v·i=0

a,b,c·1,0,0=0(Substitution)

1a+0b+0c=0(Simplify)

1a=0....equaton 1

The equation (1) is satisfied fora=0.

The vectorvin3has the position vectorv=0,b,cso thatv·i=0holds.

Thus, the position vector should lie onyz-plane so thatv·i=0holds.

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