Question

10. The resultant of two vectors A and B subtends an
angle of 45° with either of them. The magnitude of
the resultant is
(a) zero
(b) V2 A
(c) 4
(d) 2 A​

Answer 1

Answer:

$\sqrt{2} A$

Explanation:

$\bf{Refer\;to\;the\;attachment\;above}$

$\sf{As\;per\;your\;question,}$ $\sf{A\;is\;perpendicular\;to\;B}$$\sf{Resulting\;in\;A = B}$

$= \sqrt{(A^2 + B^2)}$

$= \sqrt{(A^2 + A^2)}$

$= \sqrt{(2A^2)}$

$= \sqrt{2} A$

Answer 2

The magnitude of the resultant vector is (b) A√2.

Given: The resultant of two vectors A and B subtends an angle of 45° with either of them.

To Find:  The magnitude of the resultant vector.

Solution:

• It is said that the resultant vector subtends an angle of 45° with either of the vectors A and B. So, the angle between vectors A and B is 90°.
• Since, vector A is perpendicular to vector B, they have the same lengths. Thus, |A| = |B|.
• The magnitude of resultant of two vectors A and B can be found using the formula,

  R = √ ( A² + B² + 2×A×B× cos Ф)  [  where Ф = angle between vectors ]

    = √ ( A² + B² + 0 )                        [ as cos 90° = 0 ]

    = √ ( A² + A²)                              [ as |A| = |B| ]

     = A√2

Hence, The magnitude of the resultant vector is (b) A√2.

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