Question

If n cap = ai cap + bj cap is perpendicular to the vector (icap + j cap) then the value of a and b may be

Answer 1

given, vector n^ = a i + b j is perpendicular to the vector (i + j).

we have to find value of a and b.

we know,

when two vectors A and B are perpendicular to each other then dot product of A and B = A.B = 0

similarly, vectors n^ = (a i + b j) and (i + j) are perpendicular to each other so, (a i + b j ).(i + j) = 0

or, a + b = 0.....(1)

we know, n^ denotes unit vector.

so, magnitude of n^ = 1

or, √(a² + b²) = 1

or, a² + b² = 1 .....(2)

from equation (1),

a² + (-a)² = 1

or, 2a² = 1

or, a = ±1/√2 and then, b = -a = $\mp$1/√2

hence, if a = 1/√2 then, b = -1/√2

and if a = -1/√2 then, b = 1/√2

Answer 2

Answer:

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