The value of b such that the scalar product of the vector ^i+^j+^k with the

Question

The value of b such that the scalar product of the vector

^i +^j +^k

with the unit vector parallel to the sum of the vectors

2^i + 4^j + 5^k

and

b^i + 2^j + 3^k

is one, is

Options:

A . -2

B . -1

C . 0

D . 1

Answer: Option D
:
D
The unit vector parallel to the sum of the vectors

2^i + 4^j - 5^k

and

b^i + 2^j + 3^k

^n = \frac{(2 + b)^i + 6^j - 2 ¨ k}{\sqrt{(2 + b)^{2}} + 6^{2} + (- 2)^{2}} = \frac{(2 + b)^i + 6^j - 2 ¨ k}{\sqrt{b^{2} + 4 b + 44}}

Now,

(^i +^j +^k)

^n

\Rightarrow 2 + b + 6 - 2 = \sqrt{b^{2} + 4 b + 44} \Rightarrow b = 1

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