Question

find the resultant of the given vectors​

Answer 1

Answer:

a) 15cm I think so this answer

Answer 2

For this question you need to know three things related to vector namely unit vector, triangle law of vector addition and the value of cos 37° and sin 37° (you will learn them eventually).

So let's begin with the first thing unit vector. For this question,all you need to know about them is that the unit vector along x axis is i cap, unit vector along y axis is j cap and the unit vector along the z axis is k cap and the magnitude of unit vector is 1.

Now, talking about the Triangle law of vector addition. See,it aint going to be of any help if I just simply write the statement of the law,so we will just discuss how to actually use it forming various cases (for two vectors).

Suppose you have two vectors A and B and they are making some angle θ with each other,so the magnitude of the resultant of two vectors can be obtained using the formula :

R² = A² + B² + 2ABcosθ

Now that's the general form,so as you can see every other quantity in the formula except angle θ is constant,so if you keep changing θ you will get the resultant magnitude for whatever case mentioned in the question.

Case 1 :

If θ = 90°

R² = A² + B² + 2ABcos (90)

R² = A² + B² + 2AB(0)

R² = A² + B²

So, just remember this above thing whenever you have two vectors perpendicular to each other.

If θ = 180°

R² = A² + B² + 2ABcos(180)

R² = A² + B² + 2AB(-1)

R² = A² + B² - 2AB

R² = (A - B)² [if you expand this, you will get the same thing as in previous step]

|R| = |A| - |B|

If θ = 0°

R² = A² + B² + 2ABcos(0)

R² = A² + B² + 2AB(1)

R² = A² + B² + 2AB

R² = (A + B)²

|R| = |A| + |B|

So, now we can solve the question.

So,i hope you know about components a bit because we need to break the vectors into components so as to have a simple question.

Let's first deal with the vector OP.

The component of the vector OP along Y axis :

OP' = magnitude of OP × sin (37°)

OP' = 5 × 3/5

OP' = 3 cm

Now the component of the OP vector along X axis :

OP" = magnitude of vector × cos (37°)

OP" = 5 × 4/5

OP" = 4 cm

Now the things are very simple.

Since OP' and QR vectors in the same direction,we can simply say that the resultant of the two will be the algebraic sum of the magnitudes.

OP' + QR = 3 + 4 = 7 cm. (let's call this magnitude of vec A)

Similarly,OP" and PQ vectors are in the same direction, hence using same logic :

OP" + PQ = 4 + 6 = 10 cm (let's call this magnitude of vec B)

Now vector A and vector B are perpendicular to each other because A lies completely on y axis and B lies completely on x axis and angle between x and y axis as we know is 90°.

So,we can use the formula for resultant of two vectors when the angle between them is 90°.

R² = A² + B²

R² = 7² + 10²

R² = 49 + 100

R² = 149

R = √149 cm

Therefore, option (c) is your required answer.