Question

which of the following vector is perpendicular to A=2i+ 3j+ 4k?
a. i+j+k
b.4i+3j-2k
c.i-3j+k
d.i+2j-2k

Answer 1

Dot products of two perpendicular vectors is zero.

Hence
2x + 3y = -4z

In option (d) value of x, y and z is 1, 2 and -2 respectively.
Substitute these values in above equation
2(1) + 3(2) = -4(-2)
2 + 6 = 8
8 = 8

Hence option (d) is correct.

Answer 2

CONCEPT

The dot product of two perpendicular vectors is zero.

GIVEN

We are given the vector A=2i+3j+4k.

FIND          

We have to find the vector perpendicular to A.

SOLUTION    

So as we know that the dot product of two perpendicular vectors is zero, we will check the dot product of the four options one by one with A.

        a. (i+j+k).(2i+3j+4k) = 2+3+4 = 9

         b. (4i+3j-2k).(2i+3j+4k) = 8+9-8 = 9

         c. (i-3j+k).(2i+3j+4k) = 2-9+4 = -3

        d. (i+2j-2k).(2i+3j+4k) = 2+6-8 = 0

So, as we get 0 with the dot product of option d with A, we can conclude that A is perpendicular to vector in option d.

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