Question

The resultant of two vectors is perpendicular to one of them and has the magnitude 4 m. If the sum of the magnitude of two vectors is 8m then their respective magnitude are
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Answer 1

Answer:

R^2=A^2+B^2+2ABcosQ

Answer 2

Answer:

The two vectors are of magnitude 5 and 13.

Explanation:

Given : The resultant of two vectors is perpendicular to one of them and has the magnitude 4 m. If the sum of the magnitude of two vectors is 8 m.

To find : Their respective magnitude?

Solution :

Let the two vectors be A and B.

The sum of the magnitude of two vectors is 8 m.

i.e. A+B=8

Let R is the resultant.

i.e. R=4

If the two vectors are placed such that the tail of B starts from the head of A. Then the resultant R is at right angled to A forms a right angled triangle with B-hypotenuse, A- Base and R is the perpendicular.

Applying Pythagoras theorem,

${B}^{2}={A}^{2}+{R}^{2}$

$(18-A)^{2}=A^{2}+12^{2}$

$324-36A+{A}^{2}={A}^{2}+144$

$324-144=36 A$

$36 A=180$

$A=\frac{180}{36}$

$A=5$

Substitute the value of A to find B,

$A+B=18\\5+B=18\\B=18-5\\B=13$

Therefore, The two vectors are of magnitude 5 and 13.