Question

Let a = (x+y)i+2j+yk and b = 3i+(4x+y+1)j+4k.

find the values of x and y such that a is perpendicular to b.

Answer 1

To make vector a perpendicular to vector b, x = -2/11 and y = -2/11.

Step-by-step explanation:

To determine the values of x and y such that vector a is perpendicular to vector b, we need to find the dot product of vectors a and b and set it equal to zero.

The dot product of two vectors can be calculated by multiplying their corresponding components and summing them up. So, the dot product of a and b is (x+y)(3) + (2)(4x+y+1) + (y)(4) = 0.

Simplifying the equation, we get 3x+3y+8x+2y+2 = 0. Combining like terms, we have 11x+5y+2 = 0.

So, the values of x and y that make a perpendicular to b are x = -2/11 and y = -2/11.