If the resultant of three forces F-1- - p - - 3 - - k- F-2- - 6 - - k- and F-3- - - 5 - - - - 2 k- acting on a particle has a magnitude equal to 5 units- then the value of p is

The correct options are B 4 C 2 Let R⃗ be the resultant. #160;Then R⃗ = R⃗_⃗1⃗ + #160;F⃗_⃗2⃗ + #160;F⃗_⃗3⃗ = (p + 1) î + 4 ĵ Given, ...

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Standard XII

Mathematics

Applications of Dot Product

If the result...

Question

If the resultant of three forces $_{1} = p^i + 3^j -^k,_{2} = 6^i -^k$ and $_{3} = - 5^i +^j + 2^k$ acting on a particle has a magnitude equal to 5 units, then the value of p is

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Solution

The correct options are
B $- 4$
C $2$
Let $\to R$ be the resultant.

Then
$\to R =_{1} +_{2} +_{3} = (p + 1)^i + 4^j$

Given, $| \to R | = 5$ .

Therefore,
$(p + 1)^{2} + 16 = 25$

or $p + 1 = \pm 3$

or $p = 2, - 4$

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If the resultant of three forces →F1=p^i+3^j−^k,→F2=6^i−^k and →F3=−5^i+^j+2^k acting on a particle has a magnitude equal to 5 units, then the value of p is

The correct options are B −4 C 2Let →R be the resultant. Then→R=→R1+→F2+→F3=(p+1)^i+4^jGiven, |→R|=5. Therefore,(p+1)2+16=25or p+1=±3or p=2,−4

If the resultant of three forces $_{1} = p^i + 3^j -^k,_{2} = 6^i -^k$ and $_{3} = - 5^i +^j + 2^k$ acting on a particle has a magnitude equal to 5 units, then the value of p is

The correct options are
B $- 4$
C $2$
Let $\to R$ be the resultant.

Then
$\to R =_{1} +_{2} +_{3} = (p + 1)^i + 4^j$

Given, $| \to R | = 5$ .

Therefore,
$(p + 1)^{2} + 16 = 25$

or $p + 1 = \pm 3$

or $p = 2, - 4$