Question

If a = 4i +3j and b are two vectors perpendicular to each other in the x-y plane . Find all the vectors in the same plane having projection 1 and 2 along a and b respectively

Answer 1

a and b are two vectors perpendicular to each other in xy plane.

so, a.b = 0

let b = xi + y j

so, (4i + 3j).(xi + y j) = 0

or, 4x + 3y = 0......(1)

x = 3 y = -4

then, b = k(3i - 4j) , where k is constant.

Let α = (p i + q j) is required vector.

now, projection of α along a = (α.a)/|a| = 1

or, 1 = (pi + qj).(4i + 3j)/5

or, 5 = 4p + 3q ......(1)

again, projection of α on b = (α.b)/|b| = 2

or, 2 = (pi + qj)k(3i - 4j)/5k

or, 10 = 3p - 4q ......(2)

now, from equations (1) and (2),

p = 2 and q = -1

so, required vector is α = (2i - j)

Answer 2

Answer:-2/5i cap +11/5j cap

2 i cap - j cap

Explanation:

Both answers are possible