Question

For any two vectors A and B. if A.B = AXB, the magnitude of C=A+B is equal to
(C)
(D) VA+B+ 2 x AB
(A+ B+
A+B
(B)
(A) VA+B2​

Answer 1

it is given that A.B = |A × B|

we know, dot product of two vectors p and q is written as , p.q = |p|.|q|cosθ, where θ is angle between p and q.

similarly, cross product of two vectors p and q is written as , p × q = |p|.|q|sinθ ñ, where ñ is unit vector of p × q.

so, |p × q| = |p|.|q|sinθ

from above explanation,

A.B = |A|.|B|cosθ and |A × B| = |A|.|B|sinθ

now, A.B = |A × B|

⇒|A|.|B|cosθ = |A|.|B|sinθ

⇒cosθ = sinθ

⇒tanθ = 1 = tan45°

so, θ = 45°

now, magnitude of C = A + B = √{|A|² + |B|² + 2|A||B|cos45°}

= √{|A|² + |B|² + √2|A||B|} [Ans]

Answer 2

Answer:

Explanation:

See question 138