Three vectors are given by a^vector = 3.00 icirc + (2.00) jcirc + (0) k^Hat, b^v

Question

Three vectors are given by a^vector = 3.00 icirc + (2.00) jcirc + (0) k^Hat, b^vector = 5.00 icirc + (-3.00) jcirc + (2.00) k^Hat, and c^vector = 3.00 icirc + (-1.00) jcirc + (2.00) k^Hat. Find a^vector middot (b^vector times c^vector) a^vector middot (b^vector + c^vector), x-component, y-component, and z-component of a^vector times (b^vector + c^vector) respectively. Number _______ Units _______ Number _______ Units _______ Number _______ Units _______ Number _______ Units _______ Number _______ Units _______

Explanation / Answer

here,

a = 3 i + 2 j

b = 5 i - 3 j + 2 k

c = 3 i - j + 2 k

a)

a.(b X c) = (3 i + 2 j).((5 i - 3 j + 2 k) X (3 i - j + 2 k))

=> (3 i + 2 j). ( - 15 k - 10 j - 10 k + 4 i)

=> (12 - 20) = - 8 units

b)

a.(b + c) = (3 i + 2 j).((5 i - 3 j + 2 k) + (3 i - j + 2 k))

=> (3 i + 2 j ) . ( 8 i - 4 j + 4 k)

=> 16 units

c)

a X ( b + c ) = (3 i + 2 j)X((5 i - 3 j + 2 k) + (3 i - j + 2 k))

=> (3 i + 2 j ) X ( 8 i - 4 j + 4 k)

=> ( - 12 k - 8 j - 16 k + 8 i)

=> ( 8 i - 8 j - 28 k) units

x component is 8 units

d)

y component is - 8 units

e)

z component is - 28 units

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