Given vectors a= 3i -4j+4k and b= 2i +3j -7k.
Displacement vector can be found by subtracting vector a from vector b.
Displacement vector = vector b - vector a.
Plugging values of vector a and vector b in above formula.
Displacement vector = (2i +3j -7k) - (3i -4j+4k).
Distributing minus sign over second parenthese, we get
Displacement vector = 2i +3j -7k - 3i +4j -4k = -i +7j -11k
We know formula for magnitude of a vector
[tex]\sqrt{x^2+y^2+z^2}[/tex], where x, y and z are the coefficents of i, j and k there.
<a> = < 3 -4 4 > and
<b> = < 2 3 -7 >
[tex]|a|=\sqrt{(3)^2+(-4)^2 +(4)^2}=\sqrt{9+16+16}=\sqrt{41}[/tex]
[tex]|b|=\sqrt{(2)^2+(3)^2 +(7)^2}=\sqrt{4+9+49}=\sqrt{62}[/tex]
