If A⃗=B⃗+C⃗ and the magnitudes of A⃗, B⃗ and C⃗ are 5,4 and 3 units respectively, the angle betw

step 1 Hi, hi everyone. Once on this question, we'll be learning about basic concept of the vectors and

If A⃗=B⃗+C⃗ and the magnitudes of A⃗, B⃗ and C⃗ are 5,4 and...

If $\vec{A}=\vec{B}+\vec{C}$ and the magnitudes of $\vec{A}, \vec{B}$ and $\vec{C}$ are 5,4 and 3 units respectively, the angle between $\vec{A}$ and $\vec{C}$ is (a) $\cos ^{-1}\left(\frac{3}{5}\right)$ (b) $\cos ^{-1}\left(\frac{4}{5}\right)$ (c) $\frac{\pi}{2}$ (d) $\sin ^{-1}\left(\frac{3}{4}\right)$

If $\vec{A}=\vec{B}+\vec{C}$ and the magnitudes of $\vec{A}, \vec{B}$ and $\vec{C}$ are 5,4 and 3 units respectively, the angle between $\vec{A}$ and $\vec{C}$ is
(a) $\cos ^{-1}\left(\frac{3}{5}\right)$
(b) $\cos ^{-1}\left(\frac{4}{5}\right)$
(c) $\frac{\pi}{2}$
(d) $\sin ^{-1}\left(\frac{3}{4}\right)$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Vector Addition

Vector addition involves combining two or more vectors to produce a resultant vector. In problems like these, the relationship A = B + C helps establish connections between their magnitudes and directions, leading to useful insights when examining the geometrical arrangement of the vectors.

Dot Product

The dot product is a scalar product of two vectors that relates them to the cosine of the angle between them. It is defined as the product of their magnitudes and the cosine of the angle between them. This concept is crucial in determining angles between vectors, as it provides a straightforward method for expressing the relationship between magnitudes and directional cosines.

Calculating the Angle Between Vectors

To find the angle between vectors, one typically uses the dot product formula. By rearranging the dot product formula to solve for cosine of the angle, the process involves dividing the dot product by the product of the magnitudes of the vectors. This technique is fundamental in many vector analysis problems and provides a method for quantifying the directional relationship between vectors.

Transcript

Please give Ace some feedback