Question

find the projectile of A =2i-6j+4k onto the direction of B=7i-8j-9k
answer please
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Answer 1

Given:

$\vec{A}$ = 2i - 6j + 4k

$\vec{B}$ = 7i - 8j + 9k

To find:

Projection on vector $\vec{A}$ on $\vec{B}$.

Solution:

The projection of vector $\vec{A}$ on the direction of $\vec{B}$ is -

            $Projection = \frac{\vec {A} \vec{B}}{IBI}$    -(1)

here, $\vec{A}$ = 2i - 6j + 4k

         $\vec{B}$ = 7i -8j -9k

first calculate $\vec{A} \cdot \vec{B}$, we have

 $\vec{A} \cdot \vec{B}$ = (2i -6j + 4k).(7i - 8j - 9k)

          = (2×7)(i×i) - (2×8)(i×j) - (2×9)(i×k) - (6×7)(j×i) + (6×8)(j×j) + (6×9)(j×k) +

              (4×7)(k×i) - (4×8)(k×j) - (4×9)(k×k)

as we know,

i×i = 1, i×j=0, i×k=0

j×j = 1, j×i=0, j×k=0

k×k =1, k×i=0, k×j=0

so, $\vec{A} \cdot \vec{B}$ = 14 + 48 - 63

              = 1

and,

  $IBI$ = $\sqrt{7^2 + (-8)^2 + (-9)^2}$

         = $\sqrt{49 + 64 + 81}$

         = $\sqrt{194}$

         = 14

So, putting all the values in equation (1), we get

  $Projection = \frac{\vec {A} \cdot \vec {B}}{IBI}$

                     = $\frac{1}{14}$

Therefore, projection of $\vec{A}$ on direction of $\vec{B}$ will be $\frac{1}{14}$.

Answer 2

Answer:

Explanation:

Given that vector a=2i-6j+4k onto the direction of vector b=7i-8j-9k

Then as we know that projection of vector a on vector b = a•b/|b|

So, projection of given vector(2i–6j +4k) on vector(7i–8j–9k) =

(2i–6j +4k)•(7i–8j–9k)/|7i–8j–9k|

=(14 +48–36)/√{7²+(-8)²+(-9)²}

Because i•i=j•j=k•k=1 & i•j=j•k=k•i=0

=26/√(49+64+81)

=26/√194,Ans.

I hope it helps you…!!!