The components of vector $i + j + k$ along vector $i + 2 j + 3 k$ is

(3 / 7) (i + 2 j + 3 k)

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

(i + 2 j + 3 k)

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

(1 / 7) (i + 2 j + 3 k)

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

(4 / 7) (i + 2 j + 3 k)

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

Open in App

Solution

The correct option is B $(3 / 7) (i + 2 j + 3 k)$
The projection of vector $i + j + k$ along vector, $i + 2 j + 3 k$ is
$= \frac{(i + j + k) \cdot (i + 2 j + 3 k)}{| i + 2 j + 3 k |} = \frac{6}{\sqrt{14}}$
Hence component of vector $i + j + k$ along $i + 2 j + 3 k$ is,
$= \frac{6}{\sqrt{14}} . \frac{i + 2 j + 3 k}{| 1 + 2 j + 3 k |} = \frac{3}{7} (i + 2 j + 3 k)$

Suggest Corrections

Similar questions

(i - 2 j + 3 k) \times (2 j - 3 k)

[(3 i - 2 j - 2 k) \times (i - k)] \times [(i + j + k) \times (i - 2 j + 3 k)]

ˆ i - 2 ˆ j + 3 ˆ k

3 ˆ i - 2 ˆ j + ˆ k

\vec{r} = \hat{i} - \hat{j} + λ (\hat{i} + \hat{j} + \hat{k}) + μ (\hat{i} - 2 \hat{j} + 3 \hat{k})

\vec{r} \cdot (5 \hat{i} - 2 \hat{j} - 3 \hat{k}) = 7

\vec{r} \cdot (5 \hat{i} + 2 \hat{j} - 3 \hat{k}) = 7

\vec{r} \cdot (5 \hat{i} - 2 \hat{j} + 3 \hat{k}) = 7

3 \hat{i} + \hat{j} - \hat{k}, 2 \hat{i} - \hat{j} + 7 \hat{k} and 7 \hat{i} - \hat{j} + 23 \hat{k}

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

Join BYJU'S Learning Program