If a vectors = 2 i – 4 j + 5 k then find value of lamda so that lamda times a (vector) may be a unit vector

 i  j and k are unit vector/axis

Asked by haroonrashidgkp | 23rd Oct, 2018, 07:06: PM

Expert Answer:

L e t space A with rightwards harpoon with barb upwards on top space equals 2 i with hat on top space minus 4 j with overbrace on top space plus 5 k with overbrace on top space
u n i t space v e c t o r space A with hat on top space equals stack fraction numerator A over denominator open vertical bar A close vertical bar end fraction with rightwards harpoon with barb upwards on top
open vertical bar A close vertical bar equals square root of 2 squared plus 4 squared plus 5 squared end root equals square root of 4 plus 16 plus 25 end root space equals square root of 45

S o space u n i t space v e c t o r space A with hat on top space equals space fraction numerator 2 i with hat on top space minus 4 j with overbrace on top space plus 5 k with overbrace on top over denominator square root of 45 end fraction space
h e n c e space A with hat on top space equals fraction numerator 1 over denominator square root of 45 end fraction space left parenthesis 2 i with hat on top space minus 4 j with overbrace on top space plus 5 k with overbrace on top right parenthesis
lambda equals fraction numerator 1 over denominator square root of 45 end fraction

Answered by Ram Singh | 28th Oct, 2018, 01:06: PM