Single Choice

What displacement must be added to the displacement $$25\hat i-6\hat j\ m$$ to give a displacement of $$7.0\ m$$ pointing in the $$x-$$ direction

A$$18\hat i-6\hat j$$
B$$32\hat i-13\hat j$$
C$$-18\hat i+6\hat j$$
Correct Answer
D$$-25\hat i+13\hat j$$

Solution

Given Vector = $$25 i - 6 j$$

Resultant Vector = 7 m in the direction of x axis.

We know that x axis refers to the direction in terms of i

So the Resultant vector can be written as 7 i

So Original Vector + Some Vector =$$ 7 i$$
Let the Some vector be denoted by V.

=>$$ 25 i - 6 j + V = 7 i$$

Transposing the terms other than V to the Left Hand Side we get,

=>$$ V = 7 i - ( 25 i - 6 j )$$

=> $$V = 7 i - 25 i + 6 j$$

=> $$V = -18 i + 6 j$$

Hence the unknown vector to be added is $$ -18 i + 6 j$$.

Hence option (c) is correct.

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