Question

if resultant of two vectors a and b is √7b.the value of b\a is

Answer 1

Answer:

The correct answer to this question is $\frac{b}{a} = \frac{1}{2}$

Explanation:

Given - Resultant of two vectors a and b is √7b.

To Find - Find the value of b\a.

Now, the Resultant vector - $R^{2} = A^{2} + B^{2} + 2ABCos$θ

The given values are -

$($√7b$)^{2}$ = $a^{2} + b^{2} + 2abCos60$°

$7b^{2} = a^{2} + b^{2} + 2ab\frac{1}{2}$

$7b^{2} = a^{2} + b^{2} + ab$

$a^{2} + b^{2} + ab -7b^{2} = 0$

$a^{2} -6b^{2} + ab = 0$

Now. rearranging the above equation,

$a^{2} + ab -6b^{2} = 0$

$a^{2} +3ab - 2ab - 6b^{2} = 0$

$a(a + 3b) -2b(a+3b) = 0$

$(a - 2b) (a + 3b) = 0$

Thus, $a - 2b = 0$

hence, $a = 2b \\\frac{a}{b}= 2$

Therefore, the value of $\frac{b}{a} = \frac{1}{2}$

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