Question

P vextor is a unit vector and (x-p).(x+p)=80 find |x|

Answer 1

|X| = 9  

Step-by-step explanation:

as the dot product has distributive property:

that is U . (V+W) = U.V + U.W

(X-P). (X+P)  =    (X). (X+P)   - (P). (X+P)            // using above distributed law

                 = X.X + X.P - P.X - P.P   .................... eq 1

since p is unit vector P.P =1

X.X = |X| ²

X.P = P.X                , SO that       X.P - P.X = 0

eq 1 becomes

|X| ² - 1  = 80

|X| ² = 81

|X| = 9                      // taking +ve value