How to find many vectors orthogonal to given in vector three space

Coplanar vectors problems can be solved using two different strategies as shown in the video. Consider linear combination of scalar triple product of vectors.
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[StreuB]

This was absolutely PERFECT!!! Thank you so so much!! :-)


Now, what if you needed to pick two vectors that are in opposite directions (colinear?) I would assume it would be best to pick one of the values to be 0 so that the resulting vector will be anchored to a given plane and then taking the ± operator of that vector?

[goplay]

What if I had to find a unit vector orthogonal to this vector??

[robelweldegebrial]

thank you I will subscribe you channel.

[GioZane]

Might have been more appropriate to write v as a column vector to denote orthogonality?

[uditbansal]

SIR CAN U SOLVE THAT QUESTION I AM GETTING PROBLEM IN GIVEN QUESTION:

Q) Suppose that W1 and W2 are subspaces of V such that dimW1 < dimW2. Prove that there is a nonzero vector in W2 which is orthogonal to all vectors in W1.

PLEASE REPLY AS SOON AS POSSIBLE SIR.
IF ANYONE WHO KNOWS THAT QUESTION PLS SEND THE SOLUTION OF ABOVE QUS.

[StewieGriffin]

dot product formula
lets say a vector we want to find is denoted x
find a vector orthogonal to v = <1, 2, 3, >


v1x1+v2x2+v3x3 = 0
x1 +2 x2+3 x3 = 0


Trivial solution would be
x = <0, 1, -2/3>
Any scalar multiplied to this vector will give you every vector orthogonal to v