Find the area of a triangle whose vertices are A(i-k), B(2i+j+k),C(j+2

1.	Find the area of a triangle whose vertices are A(i-k), B(2i+j+k),C(j+2k)
Answer» The vector AB = i+j+2k The vector AC = - i+j+3k The area of triangle ∆=(1/2)\|AB×AC\|= (1/2)\|(i+j+2k)×(-i+j+3k)\| =(1/2)\|-i×i-j×i-2k×i +i×j+j×j+2k×j+3i×k+3j×k+6k×k\| =(1/2)\|0+k-2j+k+0-2i-3j+3i+0\| =(1/2)\|i -5j+2k\| =(1/2)√(1+25+4) =(1/2)√(30)

Find the area of a triangle whose vertices are A(i-k), B(2i+j+k),C(j+2k)

Answer»

The vector AB = i+j+2k

The vector AC = - i+j+3k

The area of triangle

∆=(1/2)|AB×AC|= (1/2)|(i+j+2k)×(-i+j+3k)|

=(1/2)|-i×i-j×i-2k×i +i×j+j×j+2k×j+3i×k+3j×k+6k×k|

=(1/2)|0+k-2j+k+0-2i-3j+3i+0|

=(1/2)|i -5j+2k|

=(1/2)√(1+25+4)

=(1/2)√(30)

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Find the area of a triangle whose vertices are A(i-k), B(2i+j+k),C(j+2k)

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