Q. 234.5( 2 Votes )

Dot product of a vector with vectors and are respectively 4, 0 and 2. Find the vector.[CBSE 2013]

Answer :

Vectors:





Their Dot products are 4, 0 and 2.


Calculation:


Let the required vector be,



Now,




x - y + z = 4 …Eq. 1


Similarly




2x + y - 3z = 0 …Eq. 2




x + y + z = 2 …Eq. 3


Subtract Eq. 1 from Eq. 3


(x + y + z) – (x - y + z) = 2 - 4


2y = -2


y = - 1


Now putting the value of y in equation(2) and equation (3) we get,


2 x – 3 z = 1 …(Eq(4))


x + z = 3 ……(Eq(5))


Eq(4) – 2 × Eq (5)


- 5 z = - 5


z = 1


Now putting value of z in equation (1) we get,


x – y + z = 4


x + 1 + 1 = 4


x = 2


So the vector is,


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