Question

Which of the following vector is perpendicular to A = i +2j-k?
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Answer 1

Answer:

Let the vector be called v, so, v=i^-2j^+k^. Let the required vector be called a such that a=x*i^+y*j^+z*k^……..(1). So, for being a perpendicular to v, a.v=0

or, x-2y+z=0……(2)

For any (x,y,z) triplet that satisfies equation (2) gives the required vector, a. So, the solution for the value of vector, a is infinite. For example, if we take,z=-1, then from equation (2), x-2y=1…... (3). Now, let us take, y=1, then from equation (3), x=2y+1=2×1+1=3. So, (x,y,z)=(3,1,-1). Now, putting these values of x,y and z in eqn. (1), we get, a=3i^+j^-k^. Similarly, many such values for the triplet(x,y,z) can be chosen which satisfies eqn. (2) and yield different expression for vector a like the one cited above. All these vectors are perpendicular to the given vector, v. (Answer)