The position of a particle is given by r⃗=î+2 ĵ-k and its linear momentum is given by p⃗=3 î+4 ĵ

step 1 In this question we have given a position vector and momentum vector of a particle and we have t

The position of a particle is given by r⃗=î+2 ĵ-k and its...

The position of a particle is given by $\vec{r}=\hat{i}+2 \hat{j}-k$ and its linear momentum is given by $\vec{p}=3 \hat{i}+4 \hat{j}-2 \hat{k}$.
Then its angular momentum about the origin is perpendicular to
(a) $x$-axis
(b) $y$-axis
(c) $z$-axis
(d) $y z$-plane

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Key Concepts

Angular Momentum

Angular momentum is a vector quantity that represents the rotational analogue of linear momentum. It is defined as the cross product of a particle's position vector and its linear momentum vector. This concept is fundamental in rotational dynamics and describes how the distribution of mass and velocity contributes to the overall 'twisting' effect around a point or axis.

Cross Product

The cross product is a binary operation on two vectors in three-dimensional space that results in a third vector perpendicular to the plane containing the original vectors. Its magnitude is determined by the product of the magnitudes of the two vectors and the sine of the angle between them. The direction of the cross product follows the right-hand rule, making it a crucial tool in calculating quantities like angular momentum.

Vector Orthogonality

Vector orthogonality refers to the concept of two vectors being perpendicular to each other, meaning their dot product is zero. In the context of cross products, the resulting vector is inherently orthogonal to both of the initial vectors. This property is widely applied in physics and engineering to analyze and solve problems involving forces, motion, and rotations.

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