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Question

Find a vector of magnitude 5 units and parallel to the resultant of the vectors a=2^i+3^j^k and b=^i2^j+^k.

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Solution

Given vectors a=2^i+3^j^k and b=^i2^j+^k.
Let c be the resultant of a and b.
c=a+b=(2^i+3^j^k)+(^i2^j+^k) c=3^i+^j+0^k
Comparing with X=x^i+y^j+z^k
|c|=x2+y2+z2=32+12=9+1=10
Unit vector in the direction of c, ^c=c|c|=3^i+^j10
Hence, the vector of magnitude 5 units and parallel to the resultant of vectors a and b is ± 5 ^c=± 5110 (3 ^i+^j)=±3102 ^i±102 ^j


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