Two vectors A⃗ and B⃗ are such that A⃗+B⃗=C⃗ and A^2+B^2=C^2 If θis the angle between positive d

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Two vectors A⃗ and B⃗ are such that A⃗+B⃗=C⃗ and A^2+B^2=C^2...

Two vectors $\vec{A}$ and $\vec{B}$ are such that $\vec{A}+\vec{B}=\vec{C}$ and $A^{2}+B^{2}=C^{2}$ If $\theta$ is the angle between positive direction of $\vec{A}$ and $\vec{B}$ then the correct statement is (B) $\theta=\frac{2 \pi}{3}$ (A) $\theta=\pi$ (C) $\theta=0$ (D) $\theta=\frac{\pi}{2}$

Two vectors $\vec{A}$ and $\vec{B}$ are such that $\vec{A}+\vec{B}=\vec{C}$ and $A^{2}+B^{2}=C^{2}$
If $\theta$ is the angle between positive direction of $\vec{A}$ and $\vec{B}$ then the correct statement is (B) $\theta=\frac{2 \pi}{3}$
(A) $\theta=\pi$
(C) $\theta=0$
(D) $\theta=\frac{\pi}{2}$

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Key Concepts

Orthogonality

Orthogonality in vector algebra implies that two vectors are perpendicular to each other. Mathematically, this condition is met when the dot product of the two vectors is zero, indicating that the cosine of the angle between them is zero and hence the angle is 90 degrees.

Angle between Vectors

The angle between two vectors quantifies the directional difference between them. It can be determined using the dot product formula by dividing the dot product of the vectors by the product of their magnitudes and taking the inverse cosine of the result. This angle is crucial for understanding the relationship between vectors in various mathematical and physical contexts.

Vector Addition

Vector addition refers to the process of combining two or more vectors to determine a resultant vector. This process involves adding the corresponding components of the vectors, which gives the resultant vector's magnitude and direction based on the tip-to-tail rule.

Dot Product

The dot product is an operation that takes two vectors and returns a scalar. It is calculated as the product of the magnitudes of the vectors and the cosine of the angle between them. This concept is especially useful for determining the angle between two vectors and for verifying orthogonality.

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