You visited us 1 times! Enjoying our articles? Unlock Full Access!

Dot Product of Two Vectors

The sides of ...

Question

The sides of a parallelogram are $2 i + 4 j - 5 k$ and $i + 2 j + 3 k .$ Find the unit vectors parallel to the diagonals.

\frac{3 i + 6 j - 2 k}{\sqrt{49}} .

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{- 3 i - 6 j + 2 k}{\sqrt{49}} .

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{- i - 2 j + 8 k}{\sqrt{69}} .

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{i + 2 j - 8 k}{\sqrt{69}} .

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $\frac{- i - 2 j + 8 k}{\sqrt{69}} .$
$\to A B = 2 i + 4 j - 5 k = 2, 4 - 5 \to A D = i + 2 j + 3 k = 1, 2, 3$
$∴ \to A C = \to A B + \to B C = 3, 6, - 2$
$∴$ Unit vector along AC
$\frac{\to A C}{| A C |} = \frac{3, 6, - 2}{\sqrt{(9 + 36 + 4)}} = \frac{3 i + 6 j - 2 k}{7}$

Similarly $\to B D = \to A D - \to A B = - 1, - 2, 8.$
$∴$ Unit vector along BD
$\frac{\to B D}{∣ ∣ \to B D ∣ ∣} = \frac{- 1, - 2, 8}{\sqrt{(1 + 4 + 64)}} = \frac{- i - 2 j + 8 k}{\sqrt{69}} .$

Suggest Corrections

Similar questions

\vec{a} = \hat{i} + 2 \hat{j} - \hat{k}, \vec{b} = 3 \hat{i} + 2 \hat{j} + 7 \hat{k}, \vec{c} = 5 \hat{i} + 6 \hat{j} + 5 \hat{k}

\vec{a} = - 4 \hat{i} - 6 \hat{j} - 2 \hat{k}, \vec{b} = - \hat{i} + 4 \hat{j} + 3 \hat{k}, \vec{c} = - 8 \hat{i} - \hat{j} + 3 \hat{k}

\hat{a} = \hat{i} - 2 \hat{j} + 3 \hat{k}, \hat{b} = - 2 \hat{i} + 3 \hat{j} - 4 \hat{k}, \hat{c} = \hat{i} - 3 \hat{j} + 5 \hat{k}

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

2 \hat{i} + \hat{k} and \hat{i} + \hat{j} + \hat{k}

3 \hat{i} + 4 \hat{j} and \hat{i} + \hat{j} + \hat{k}

2 \hat{i} + 3 \hat{j} + 6 \hat{k} and 3 \hat{i} - 6 \hat{j} + 2 \hat{k}

a = i - 2 j + 3 k, b = 3 i - 6 j + 9 k

a = - 2 i - 4 k, b = i - 2 j - k, c = i - 4 j + 3 k

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

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

¯ i + 2 ¯ j + 3 ¯ ¯¯ ¯ k,

3 ¯ i + 4 ¯ j + 7 ¯ ¯¯ ¯ k,

- 3 ¯ i - 2 ¯ j - 5 ¯ ¯ ¯ k

Join BYJU'S Learning Program