Vector Algebra

Let c be the projection vector of b= i+4 k, >0, on the vector a= i+2 j+2 k. If | a+ c|=7, then the area of the parallelogram formed by the vectors b and c is .

Answer

16

Solution

The projection of b on a lies along a: c= a b| a|2 a= +89 a.

| a+ c|= +179 3=7 =4, so b=4 i+4 k, c= 43 a

[figure]

Area =| b c|= 43| b a|, and b a=(-8,-4,8) has magnitude 12

Area = 43 12=16

Answer: 16