Question

Force (3i - 2j+ k)N, produces a displacement of (2i – 4j+ck) m. The work done is 16 J.
Then c =

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Answer 1

Answer :

• c = 2

Given :

• Force, F = ( 3 i - 2j + k )  N
• displacement, S = ( 2i - 4j + ck )  m
• Work done , W = 16  J

To find :

• value of c

Knowledge required :

• Dot Product of two vectors with orthogonal notation

Let , there are two vectors

A = ai + bj + ck   and

B = di + ej + fk

then,

A.B = ad + be + cf

( it is because dot product of any orthogonal vector with itself is always 1 and dot product of any orthogonal vector with another orthogonal vector is always zero. )

Solution :

As we know,

→  Work = Force × Displacement

so,

→ W = ( 3 i - 2 j + k ) . ( 2 i - 4 j + c k )

→ W = (3)(2) + (-2)(-4) + (1)(c)

→ W = 6 + 8 + c

→ W = 14 + c

It is given that work done is equal to 16 J

so,

→ 16 = 14 + c

→ c  =16 - 4

→ c = 2

Therefore,

Value of c is 2 .

Answer 2

Answer:

Explanation:

Force, F = ( 3 i - 2j + k )  N

displacement, S = ( 2i - 4j + ck )  m

Work done , W = 16  J