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Representation of Vectors

14. Given =3 ...

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14. Given =3 - j b=2+j-3k Express b = b1 +b2 where b1 is parallel to and b2 isperpendicular to (a, b, b1, b2 are vectors)

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\to a = 2 ˆ i - ˆ j - 2 ˆ k

\to b = 7 ˆ i + 2 ˆ j - 3 ˆ k

\to b

\to b =_{1} +_{2}

_{1}

\to a

_{2}

is perpendicular to

\to a

\to a = 2^i -^j - 2^k

\to b = 7^i + 2^j - 3^k,

\to b

\to b = {\to b}_{1} + {\to b}_{2},

{\to b}_{1}

\to a

{\to b}_{2}

is perpendicular to

\to a .

b = 3 j + 4 k

is to be written as the sum of a vector

b_{1}

a = i + j

b_{2}

perpendicular to

a

b_{1}

\to a = 2^i -^j - 2^k

\to b = 7^i + 2^j - 3^k,

\to b

\to b = {\to b}_{1} + {\to b}_{2},

{\to b}_{1}

\to a

{\to b}_{2}

is perpendicular to

\to a .

a - a^{3} + b^{3} - b

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