A particle has the position vector r -2 -k- and the linear momentum p -2 -k- Then- its angular momentum about the origin is A- -3 k-B- -3 k-C- -3 k-D- -5 k-

The correct option is B î+ĵ+3k̂Angular momentum, L=r×p =î amp; ĵ amp; k̂ nbsp; 1 amp; 2 amp; 1 nbsp; 2 amp; 1 amp;1 nbsp; =î( 2+1) ...

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Standard XII

Physics

Cross Product

A particle ha...

Question

A particle has the position vector $\to r =^i - 2^j +^k$ and the linear momentum $\to p = 2^i -^j +^k$ . Then, its angular momentum about the origin is

-^i +^j - 3^k

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-^i +^j + 3^k

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^i +^j + 3^k

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^i -^j - 5^k

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Solution

The correct option is B $-^i +^j + 3^k$
Angular momentum, $\to L = \to r \times \to p$
$= ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 1 & - 2 & 1 2 & - 1 & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣$
$=^i (- 2 + 1) -^j (1 - 2) +^k (- 1 + 4)$
$= -^i +^j + 3^k$

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Similar questions

Q. A particle has the position vector

\to r =^i - 2^j +^k

and the linear momentum

\to p = 2^i -^j +^k

. Then, its angular momentum about the origin is

Q. Let

\to α =^i +^j +^k, \to β =^i -^j -^k

and

\to γ = -^i +^j -^k

be three vectors. A vector

\to δ,

in the plane of

\to α

and

\to β,

whose projection on

\to γ

\frac{1}{\sqrt{3}},

is given by

Q. A unit vector perpendicular to the plane containing the vector

^i + 2^j +^k

and

- 2^i +^j + 3^k

Q. The points

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

are

Let $\to a =^i +^j +^k, \to b =^i -^j +^k$ and $\to c =^i -^j -^k$ be three vectors. A vector $\to v$ in the plane of
$\to a$ and $\to b$ , whose projection on $\to c$ is $\frac{1}{\sqrt{3}}$ , is given by

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Cross Product

Standard XII Physics

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A particle has the position vector →r=^i−2^j+^k and the linear momentum →p=2^i−^j+^k. Then, its angular momentum about the origin is

The correct option is B −^i+^j+3^kAngular momentum, →L=→r×→p =∣∣ ∣ ∣∣^i^j^k1−212−11∣∣ ∣ ∣∣ =^i(−2+1)−^j(1−2)+^k(−1+4) =−^i+^j+3^k

A particle has the position vector $\to r =^i - 2^j +^k$ and the linear momentum $\to p = 2^i -^j +^k$ . Then, its angular momentum about the origin is

The correct option is B $-^i +^j + 3^k$
Angular momentum, $\to L = \to r \times \to p$
$= ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 1 & - 2 & 1 2 & - 1 & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣$
$=^i (- 2 + 1) -^j (1 - 2) +^k (- 1 + 4)$
$= -^i +^j + 3^k$