Question

Find a.b,when a=i-j+5k and b=3i-2k

Answer 1

Answer:

the answer is in the image

Answer 2

Given :-

$\rm \vec{a} = \hat{i} - \hat{j} + 5 \hat{k} \\ \\ \rm \vec{b} = 3 \hat{i} - 2 \hat{k}$

To find :-

$\rm \vec{a} .\vec{b}$

Solution :-

$\longrightarrow \rm \vec{a} .\vec{b} = ( \hat{i} - \hat{j} + 5 \hat{k}) ( 3 \hat{i} - 2 \hat{k}) \\ \\ \\ \longrightarrow \rm \vec{a} .\vec{b} = ( 1 \: \hat{i} - 1 \: \hat{j} + 5 \hat{k}) ( 3 \hat{i} - 2 \hat{k}) \\ \\ \\ \longrightarrow \rm \vec{a} .\vec{b} = ( 1 \times 3) - ( 1 \times 0) - (5 \times 2) \\ \\ \\ \longrightarrow \rm \vec{a} .\vec{b} = 3 - 0 - 10 \\ \\ \\ \longrightarrow \rm \vec{a} .\vec{b} = - 7$

Answer :-

-7

Additional Information :-

Dot product of two vectors (m and n) with angle x° :-

⏺️m.n = |m| |n| cos x