Question

Find unit vector which are perpendicular to both the vectors
2i^ + j^ -k^ and 3i^ +4j^ -k^​

Answer 1

Answer:

$\dfrac{3i -j + 4k}{\sqrt{26} }$

Method:

• Get the vector perpendicular to both using cross product of the vectors.
• Divide the vector you got as result by it's magnitude to get a unit vector in the same direction.

Cross product:

$(2i + j - k ) \times (3i + 4j -k)$

$(-1 + 4) i - (-2 + 3)j + (8-4)k\\=3i -j + 4k$

Unit vector:

$\dfrac{3i -j + 4k}{\sqrt{9+1+16} } \\=\dfrac{3i -j + 4k}{\sqrt{26} }$