A vector perpendicular to both the vectors 2 - j + 5k and
X-axis is
Answers
Given:
The vectors 2i-j+5k and x axis
To find:
A vector perpendicular to both the vectors 2i-j+5k and x axis
Solution:
If two vectors are perpendicular, then their cross-product is defined to be A × B = (a2_b3 - a3_b2, a3_b1 - a1_b3, a1_b2 - a2*b1).
The cross product of two non-parallel vectors is a vector that is perpendicular to both of them.
(a1, a2, a3) = (2, -1, 5)
(b1, b2, b3) = (1, 0, 0) (represents x-axis = 1i + 0j + 0k)
= 0i + 5j + k
∴ The vector perpendicular to both the vectors 2i-j+5k and x axis is 5j + k.
Given:
The vectors 2i-j+5k and x axis
To find:
A vector perpendicular to both the vectors 2i-j+5k and x axis
Solution:
If two vectors are perpendicular, then their cross-product is defined to be A × B = (a2_b3 - a3_b2, a3_b1 - a1_b3, a1_b2 - a2*b1).
The cross product of two non-parallel vectors is a vector that is perpendicular to both of them.
(a1, a2, a3) = (2, -1, 5)
(b1, b2, b3) = (1, 0, 0) (represents x-axis = 1i + 0j + 0k)
\begin{pmatrix}2&-1&5\end{pmatrix}\times \begin{pmatrix}1&0&0\end{pmatrix}(
2
−1
5
)×(
1
0
0
)
=\begin{pmatrix}-1\cdot \:0-5\cdot \:0&5\cdot \:1-2\cdot \:0&2\cdot \:0-(-1\cdot \:1)\end{pmatrix}=(
−1⋅0−5⋅0
5⋅1−2⋅0
2⋅0−(−1⋅1)
)
=\begin{pmatrix}0&5&1\end{pmatrix}=(
0
5
1
)
= 0i + 5j + k
∴ The vector perpendicular to both the vectors 2i-j+5k and x axis is 5j + k.