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Lesson Posted on 11 Sep Vector Algebra

Vectors and scaler

Raj Kumar

I am Six Sigma Black belt trained from American Society of Quality I am 2011 pass out in B.tech from...

Vector is that quantity that has direction and magnitude for example force, velocity, acceleration and displacement The scaler is that quantity which has the only magnitude for example speed, volume, mass temperature, power, energy and time The measure of a vector is a scalar quantity. A scalar... read more

Vector is that quantity that has direction and magnitude

for example force, velocity, acceleration and displacement

The scaler is that quantity which has the only magnitude

for example speed, volume, mass temperature, power, energy and time

The measure of a vector is a scalar quantity.

A scalar can multiply vectors. The result is another vector.

Suppose c is a scalar and v = (a, b) is a vector, then the scalar multiplication would be cv = c (a, b) = (ca, cb). Hence each component of vector gets multiplied by the scalar.

If two vectors are of the same dimension, they can be added or subtracted from each other. The result is gain a vector.

 

Some Basic Rules of Algebra of Vectors:

 

a.a = |a|2 = a2

a.b = b.a

a.0 = 0

a.b = (a cos q)b = (projection of a on b)b = (projection of b on a) a

a.(b + c) = a.b + a.c (This is also termed as the distributive law)

(la).(mb) = lm (a.b)

(a ± b)2 = (a ± b) . (a ± b) = a2 + b2 ± 2a.b If a and b are non-zero, then the angle between them is given by cos θ = a.b/|a||b|

a x a = 0

a x b = - (b x a)

a x (b + c) = a x b + a x c

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Answered on 24 Sep CBSE/Class 11/Science/Physics CBSE/Class 12/Science/Physics Vector Algebra

G Ramakrishna Krishna

it is possible only when given vector is along any coordinate axis.
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Answered on 03/12/2016 CBSE/Class 12/Science/Mathematics Tuition/Class XI-XII Tuition (PUC) Vector Algebra

Define vector?

Sarvajeet Kumar

An Experienced Trainer

Any quantity which has both magnitude and direction is called the vector quantity.
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Answered on 03/12/2016 CBSE/Class 12/Science/Mathematics Tuition/Class XI-XII Tuition (PUC) Vector Algebra

What do you mean by direction cosines?

Sarvajeet Kumar

An Experienced Trainer

X = ai + bj + ck; l=cos A=a/square root (square of a+square of b +square of c); m=cos B=b/square root (square of a+square of b +square of c); n=cos C=c/square root (square of a+square of b +square of c) l, m, n are called direction cosines of the vector X.
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Answered on 03/12/2016 CBSE/Class 12/Science/Mathematics Tuition/Class XI-XII Tuition (PUC) Vector Algebra

What do you mean by addition vectors?

Sarvajeet Kumar

An Experienced Trainer

In two given vectors, vector a and vector b. So the addition of vectors, vector c= vector a + vector b.
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Answered on 03/12/2016 CBSE/Class 12/Science/Mathematics Tuition/Class XI-XII Tuition (PUC) Vector Algebra

What is the general equation for addition of vectors?

Sarvajeet Kumar

An Experienced Trainer

In two given vectors, vector a and vector b. So, the addition of vectors, vector c= vector a + vector b.
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Answered on 03/12/2016 CBSE/Class 12/Science/Mathematics Tuition/Class XI-XII Tuition (PUC) Vector Algebra

Find the values of x, y, and z so that the vectors: vector a = x(i) + 2(j) + z(k) and vector b = 2(i)... read more
Find the values of x, y, and z so that the vectors: vector a = x(i) + 2(j) + z(k) and vector b = 2(i) + y(j) + k are equal? read less

Sarvajeet Kumar

An Experienced Trainer

2, 2, 1.
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Answered on 03/12/2016 CBSE/Class 12/Science/Mathematics Tuition/Class XI-XII Tuition (PUC) Vector Algebra

Let vector a = i + 2j and b = 2i + j. Is mod of vector a = mod of vector b?

Sarvajeet Kumar

An Experienced Trainer

mod of vector a = mod of vector b, square root (1+4)=square root (4+1), square root (5)=square root (5).
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Answered on 03/12/2016 CBSE/Class 12/Science/Mathematics Tuition/Class XI-XII Tuition (PUC) Vector Algebra

Find the unit vector in the direction of the sum of the vectors, a = 2i + 2j +5k and b = 2i + j + 3k?

Sarvajeet Kumar

An Experienced Trainer

The unit vector=4i + 3j + 8k / (square root 89).
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Answered on 03/12/2016 CBSE/Class 12/Science/Mathematics Tuition/Class XI-XII Tuition (PUC) Vector Algebra

What are the important properties of scalar product?

Sarvajeet Kumar

An Experienced Trainer

For two vectors A(a1, a2, a3) and B(b1, b2, b3) The scalar product=A.B=a1.b1+ a2.b2+ a3.b3.
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