If, 𝐀=2 𝐢̂+3 𝐣̂+4 𝐤̂ and 𝐁=4 𝐢̂+3 𝐣̂+2 𝐤̂, then angle between 𝐀 and 𝐁 is (a) sin^-1((25)/(29)) (

step 1 In this question we have given two vectors and we have to find the angle between the vectors. So

If, 𝐀=2 𝐢̂+3 𝐣̂+4 𝐤̂ and 𝐁=4 𝐢̂+3 𝐣̂+2 𝐤̂, then angle...

If, $\mathbf{A}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$ and $\mathbf{B}=4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$, then angle between $\mathbf{A}$ and $\mathbf{B}$ is (a) $\sin ^{-1}\left(\frac{25}{29}\right)$ (b) $\sin ^{-1}\left(\frac{29}{25}\right)$ (c) $\cos ^{-1}\left(\frac{25}{29}\right)$ (d) $\cos ^{-1}\left(\frac{29}{25}\right)$

If, $\mathbf{A}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$ and $\mathbf{B}=4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$, then angle
between $\mathbf{A}$ and $\mathbf{B}$ is
(a) $\sin ^{-1}\left(\frac{25}{29}\right)$
(b) $\sin ^{-1}\left(\frac{29}{25}\right)$
(c) $\cos ^{-1}\left(\frac{25}{29}\right)$
(d) $\cos ^{-1}\left(\frac{29}{25}\right)$

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Key Concepts

Angle Between Vectors

The angle between two vectors is determined using the cosine formula, which relates the dot product to the product of the magnitudes of the vectors. By rearranging this formula to compute the inverse cosine of the dot product divided by the product of the magnitudes, one can find the measure of the angle between the vectors.

Vector Magnitude

The magnitude of a vector, often called its length or norm, is a measure of its size. It is determined by taking the square root of the sum of the squares of its components, providing a basis for many vector calculations including normalization.

Vectors

Vectors are mathematical entities characterized by both magnitude and direction. They are used to represent quantities such as force, velocity, and displacement in various fields like physics and engineering.

Dot Product

The dot product is an operation that takes two vectors and returns a scalar, calculated by multiplying corresponding components and summing the results. It is a key tool in determining the relationship between two vectors, such as checking for orthogonality or calculating the angle between them.

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