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# For all real numbers a, b, c, d, e, and f, the operation Θ is defined

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Re: For all real numbers a, b, c, d, e, and f, the operation Θ is defined [#permalink]
gmatt1476 wrote:
For all real numbers a, b, c, d, e, and f, the operation Θ is defined by the equation $$(a, b, c) Θ (d, e, f) = ad + be + cf$$. What is the value of $$(1,−2, 3) Θ (1, −\frac{1}{2}, \frac{1}{3})$$ ?

A. -1

B. 5/6

C. 1

D. 5/2

E. 3

PS37631.02

As per the given conditions: $$(1,−2, 3) Θ (1, −\frac{1}{2}, \frac{1}{3})$$

1*1=1 + (-2*-1/2=1) + (3*1/3=1) = 3 Ans E
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Re: For all real numbers a, b, c, d, e, and f, the operation Θ is defined [#permalink]
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gmatt1476 wrote:
For all real numbers a, b, c, d, e, and f, the operation Θ is defined by the equation $$(a, b, c) Θ (d, e, f) = ad + be + cf$$. What is the value of $$(1,−2, 3) Θ (1, −\frac{1}{2}, \frac{1}{3})$$ ?

A. -1
B. 5/6
C. 1
D. 5/2
E. 3

PS37631.02

Given: (a, b, c) Θ (d, e, f) = ad + be + cf
So, (1,−2, 3) Θ (1, −1/2, 1/3) = (1)(1) + (-2)(-1/2) + (3)(1/3)
= 1 + 1 + 1
= 3

Cheers,
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Re: For all real numbers a, b, c, d, e, and f, the operation Θ is defined [#permalink]
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gmatt1476 wrote:
For all real numbers a, b, c, d, e, and f, the operation Θ is defined by the equation $$(a, b, c) Θ (d, e, f) = ad + be + cf$$. What is the value of $$(1,−2, 3) Θ (1, −\frac{1}{2}, \frac{1}{3})$$ ?

A. -1

B. 5/6

C. 1

D. 5/2

E. 3

PS37631.02

Plugging into the equation, we have:

1(1) + (-2)(-1/2) + 3(1/3) = 1 + 1 + 1 = 3

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Re: For all real numbers a, b, c, d, e, and f, the operation Θ is defined [#permalink]
Given (a, b, c)Θ(d, e, f) = ad + be + cf and

$$(1,−2,3)Θ(1,\frac{−1}{2},\frac{1}{3})$$ = $$(1 * 1) + (-2 * \frac{−1}{2}) + (3 * \frac{1}{3})$$

$$(1,−2,3)Θ(1,\frac{−1}{2},\frac{1}{3})$$ = 1 + 1 + 1 = 3

Option E
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For all real numbers a, b, c, d, e, and f, the operation Θ is defined [#permalink]
Top Contributor
SOLUTION:

(a,b,c)Θ(d ,e, f)=ad+ be +cf

In the expression (1,−2,3)Θ(1,−1/2,1/3) ,
a=1 d=1
b=-2 e=-1/2
c=3 f= 1/3

Using this operation, we have, ad+ be +c f

= (1.1) + (-2. -1/2) + (3.1/3)

= 1 + 1 +1

=3 (OPTION E)

Hope this helps
Devmitra Sen(Math)
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Re: For all real numbers a, b, c, d, e, and f, the operation Θ is defined [#permalink]
gmatt1476 wrote:
For all real numbers a, b, c, d, e, and f, the operation Θ is defined by the equation $$(a, b, c) Θ (d, e, f) = ad + be + cf$$. What is the value of $$(1,−2, 3) Θ (1, −\frac{1}{2}, \frac{1}{3})$$ ?

A. -1

B. 5/6

C. 1

D. 5/2

E. 3

PS37631.02

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Re: For all real numbers a, b, c, d, e, and f, the operation is defined [#permalink]
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Re: For all real numbers a, b, c, d, e, and f, the operation is defined [#permalink]
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