Question

If n=ai+bj is perpendicular to the vector (i+j ), then the value of a and b maybe

Answer 1

if two vectors A and B are perpendicular to each other. it means, dot product of vector A and vector B must be zero.

i.e., A.B = 0

here given two vectors n^ = ai + bj and m = i + j in such a way that vector n is perpendicular to vector n

so, dot product of n and m = 0

or, n.m = 0

or, (ai + bj).(i + j) = 0

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

also it is mentioned that vector n is unit vector , n^

so, magnitude of n^ = 1

or, √(a² + b²) = 1

from equation (1),

√{(-b)²+b²} = 1

or, √2b² = 1

squaring both sides ,

2b² = 1 => b = ±1/√2

so, a = -b = $\mp$1/√2

hence, answer will be

If a = 1/√2 then, b = -1/√2

and if a = -1/√2 then, b = 1/√2

Answer 2

Answer:

if two vectors A and B are perpendicular to each other. it means, dot product of vector A and vector B must be zero.

i.e., A.B = 0

Explanation:

Therefore value of a = -1/√2

b = 1/√2