If a body placed at the origin is acted upon by a force F-2k- then which of the following statements are correct

The correct option is B F⃗ makes an angle of 45 ^∘ with the z axis.Magnitude =F=√( 1 ^ 2 + 1 ^ 2 +( √( 2 ) #160;) #160;^ 2 ) =2 Angle wit ...

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Byju's Answer

Standard XII

Physics

Work Done as Dot Product

If a body pla...

Question

If a body placed at the origin is acted upon by a force $\to F = (^i +^j + \sqrt{2}^k)$ , then which of the following statements are correct

Magnitude of

\to F

(2 + \sqrt{2})

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Magnitude of

\to F

(2 \sqrt{2})

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\to F

makes an angle of

45^{\circ}

with the z-axis.

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\to F

makes an angle of

30^{\circ}

with the z-axis.

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Solution

The correct option is B $\to F$ makes an angle of $45^{\circ}$ with the z-axis.
Magnitude $= F = \sqrt{1^{2} + 1^{2} + {(\sqrt{2})}^{2}} = 2$
Angle with z-axis $= {cos}^{- 1} \frac{F_{z}}{F} = {cos}^{- 1} \frac{\sqrt{2}}{2} = 45^{o}$

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Similar questions

Q. If a body placed at the origin is acted upon by a force

\to F

(^i +^j + \sqrt{2}^k)

, then the following statements are correct?
1. Magnitude of

\to F

(2 + \sqrt{2})

.
2. Magnitude of

\to F

is 2.
3.

\to F

makes an angle of

45^{0}

with the Z-axis.
4.

\to F

makes an angle of

30^{0}

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Select the correct answer using the codes given below.

Q. If a body placed at the origin is acted upon by a force

¯ ¯¯ ¯ F = (^i +^j + \sqrt{2}^k)

, then which of the following statements are correct?
1.Magnitude of

¯ ¯¯ ¯ F

(2 + s q r t 2)

2.Magnitude of

¯ ¯¯ ¯ F

is 2
3.

¯ ¯¯ ¯ F

makes an angle of

45^{0}

with the Z-axis.
4.

¯ ¯¯ ¯ F

makes an angle of

30^{0}

with the Z-axis.
Select the correct answer using the codes given below.

Q. A force

\to F

makes an angle

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Q. If a unit vector

\to u = x^i + y^j + z^k

which makes an angle of

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with the vector

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and an angle of

60^{\circ}

with the vector

^j -^k .

Then point

P (x, y, z)

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^i - 2^j + 3^k, 2^i - 3^j + 4^k

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If a body placed at the origin is acted upon by a force →F=(^i+^j+√2^k), then which of the following statements are correct

The correct option is B →F makes an angle of 45∘ with the z-axis.Magnitude =F=√12+12+(√2)2=2Angle with z-axis =cos−1FzF=cos−1√22=45o

If a body placed at the origin is acted upon by a force $\to F = (^i +^j + \sqrt{2}^k)$ , then which of the following statements are correct

The correct option is B $\to F$ makes an angle of $45^{\circ}$ with the z-axis.
Magnitude $= F = \sqrt{1^{2} + 1^{2} + {(\sqrt{2})}^{2}} = 2$
Angle with z-axis $= {cos}^{- 1} \frac{F_{z}}{F} = {cos}^{- 1} \frac{\sqrt{2}}{2} = 45^{o}$