Question

The sum of the magnitudes of two vectors is 16N and their resultant is 8N. If the resultant be perpendicular to the smaller vector, find the magnitudes of the two vectors.
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Answer 1

Explanation:

A+B=16...(1)

tanα=

A+Bcosθ

Bsinθ

=tan90

Thus, A+Bcosθ=0⇒cosθ=−

B

A

...(2)

We also have: 8=

A

2

+B

2

+2ABcosθ

...(3)

Solving these we get, A=6N and B=10N

Answer 2

Answer:

The magnitudes of two vectors are 6 N and 10 N

Explanation:

Let x be the magnitude of smaller vector

∴ Magnitude of larger vector = 16 - x

Since Resultant is ⊥ smaller vector x

From vector triangle ABC

(16 -x)²  = x² + 8²

256 + x² - 32x = x² + 64

32x = 192

    x = 192/32 = 6 N

∴ Magnitude of smaller vector = x = 6 N

   Magnitude of larger vector = 16 - x = 10 N