Determine a vector which when added to the resultant of -A-2-5-k- and -B-3-4-k- gives unit vector along negative y direction-

Let →C is required vector which is added to the resultant of →A and →B nbsp; nbsp;and gives unit vector along negative y direction. Then →C+→A+→B= ĵ ⇒→C+ 2î ...

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Standard VII

Mathematics

Addition and Subtraction of Integers

Determine a v...

Question

Determine a vector which when added to the resultant of $\to A = 2^i + 5^j -^k$ and $\to B = 3^i - 4^j -^k$ gives unit vector along negative $y$ direction.

- 5^i -^j + 2^k

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- 5^i - 2^j + 2^k

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- 5^i -^j +^k

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5^i -^j + 2^k

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Solution

The correct option is B $- 5^i - 2^j + 2^k$
Let $\to C$ is required vector which is added to the resultant of $\to A$ and $\to B$ and gives unit vector along negative $y$ direction.
Then $\to C + \to A + \to B = -^j$
$\Rightarrow \to C + 2^i + 5^j -^k + 3^i - 4^j -^k = -^j$
$\Rightarrow \to C = - 5^i - 2^j + 2^k$
Final Answer: (A)

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Addition and Subtraction of Integers

Standard VII Mathematics

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Determine a vector which when added to the resultant of →A=2^i+5^j−^k and →B=3^i−4^j−^k gives unit vector along negative y direction.

The correct option is B −5^i−2^j+2^kLet →C is required vector which is added to the resultant of →A and →B and gives unit vector along negative y direction. Then →C+→A+→B=−^j ⇒→C+ 2^i+5^j−^k+3^i−4^j−^k=−^j ⇒→C=−5^i−2^j+2^k Final Answer: (A)

Determine a vector which when added to the resultant of $\to A = 2^i + 5^j -^k$ and $\to B = 3^i - 4^j -^k$ gives unit vector along negative $y$ direction.