Question

If a = 2i – 3j + k and b = 3i + 4j + xk are mutually perpendicular, find the value of x. ​

Answer 1

Answer:

When two vectors are perpendicular, you just gotta find their dot product and equate that to zero.

Now what's DOT Product?

Well,put simply,it is:

(ax)+(by)+(cz)

when the two given vectors are ai+bj+ck and xi+yj+zk; i,j,k being three unit vectors perpendicular to each other(representative of the coordinate axes)

Now comparing your question with the above stuff,

2i+2j+3k is equivalent to ai+bj+ck

and

3i+6k+nk=3i+0j+(6+n)k

the dot product is sum of the product of the coefficients,that is

2*3+3*(6+n)

Now equating this to zero and dividing both sides by 3, we get

2+6+n=0 which gives n=-8

hope it helps you

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