Question

Given two displacement vectors a= 3i -4j+4k and b= 2i +3j -7k. find the displacement and their magnitudes

Answer 1

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

`√(x^2+y^2+z^2)`, where x, y and z are the coefficents of i, j and k there.

<a> = < 3 -4 4 > and

<b> = < 2 3 -7 >

`|a|=√((3)^2+(-4)^2 +(4)^2)=√(9+16+16)=√(41)`

`|b|=√((2)^2+(3)^2 +(7)^2)=√(4+9+49)=√(62)`