Let a -2 i -3 j -4 k and b -3 i -4 j -5 k- Find the angle between them-

Here, a⃗ = 2i⃗+3j⃗+ 4k⃗, b⃗ = 3i⃗+4i⃗+ 5k⃗, a⃗.b⃗ = ab cos θ θ = cos^ 1a⃗.b⃗/ab = cos^ 12 × 3+ 3 × 4+4 × 5 /√((2^2+3^2+4^2))√((3^2+4^2+5^2)) =cos ^ 138/√(29)√ ...

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Byju's Answer

Standard XII

Mathematics

Vector Triple Product

Let a =2 i +3...

Question

Let $\to a = 2 \to i + 3 \to j + 4 \to k$ and $\to b = 3 i + 4 j + 5 k$ . Find the angle between them.

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Solution

Here, $\to a = 2 \to i + 3 \to j + 4 \to k,$

$\to b = 3 \to i + 4 \to i + 5 \to k,$

$\to a . \to b = a b c o s θ$

$θ = c o s^{- 1} \frac{\to a . \to b}{a b}$

= $c o s^{- 1} \frac{2 \times 3 + 3 \times 4 + 4 \times 5}{\sqrt{(2^{2} + 3^{2} + 4^{2})} \sqrt{(3^{2} + 4^{2} + 5^{2})}}$

= $c o s^{- 1} \frac{38}{\sqrt{29} \sqrt{50}} = c o s^{- 1} \frac{38}{\sqrt{1450}}$

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Similar questions

Q. Let

\vec{a} = 2 \vec{i} + 3 \vec{j} + 4 \vec{k} and \vec{b} = 3 \vec{i} + 4 \vec{j} + 5 \vec{k}

. Find the angle between them.

- A = - 2 i - - j + - k, - B = - i - - 3 j - - 5 k, - C = - 3 i - - 4 j - - 4 k

are the vertices of a triangle.

Q. Show that the points

A (2 \hat{i} - \hat{j} + \hat{k}), B (\hat{i} - 3 \hat{j} - 5 \hat{k}), C (3 \hat{i} - 4 \hat{j} - 4 \hat{k})

are the vertices of a right angled triangle.

Q. Show that the vectors

2 \to i - \to j + \to k, \to i - 3 \to j - 5 \to k, - 3 \to i + 4 \to j + 4 \to k

form the sides of a right angled triangle.

Q. Prove that the following vectors are coplanar:
(i)

2 \hat{i} - \hat{j} + \hat{k}, \hat{i} - 3 \hat{j} - 5 \hat{k} and 3 \hat{i} - 4 \hat{j} - 4 \hat{k}

(ii)

\hat{i} + \hat{j} + \hat{k}, 2 \hat{i} + 3 \hat{j} - \hat{k} and - \hat{i} - 2 \hat{j} + 2 \hat{k}

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Let →a=2→i+3→j+4→k and →b=3i+4j+5k. Find the angle between them.

Here, →a=2→i+3→j+4→k, →b=3→i+4→i+5→k, →a.→b=ab cos θ θ=cos−1→a.→bab = cos−12×3+3×4+4×5√(22+32+42)√(32+42+52) =cos−138√29√50=cos−138√1450

Let $\to a = 2 \to i + 3 \to j + 4 \to k$ and $\to b = 3 i + 4 j + 5 k$ . Find the angle between them.