Question

the sum and magnitude of two VECTOR s A and B are A+B=2i +6j+k and A-B =4i +2j -11k. Find the magnitude of each vector and their scalar product A.B

Answer 1

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Answer 2

Answer:

The magnitude of A and B is √50 and √41 and the scalar product of A and B  is -25.

Explanation:

Given that,

Sum of the vector A+B = 2i+6j+k....(I)

Difference of the vector A-B =4i+2j-11k.....(II)

From equation (I) and (II)

$\vec{2A}=6i+8j-10k$

$\vec{A}= 3i+4j-5k$

The magnitude of vector A

$\vec{A}=\sqrt{3^2+4^2+(-5)^2}$

$\vec{A}=\sqrt{9+16+25}$

$\vec{A}=\sqrt{50}$

Now put the value of vector A in equation (I)

$3i+4j-5k+\vec{B}=2i+6j+k$

$\vec{B}=-i+2j+6k$

The magnitude of vector B

$\vec{B}=\sqrt{(-1)^2+2^2+6^2}$

$\vec{B}=\sqrt{1+4+36}$

$\vec{B}=\sqrt{41}$

The scalar product of A and B

$A\dotc B=(3i+4j-5k)\dotc (-i+2j+6k)$

$A\dotc B=-3+8-30$

$A\dotc B=-25$

Hence, The magnitude of A and B is √50 and √41 and the scalar product of A and B  is -25.