Question

If a vector is equal to two ICAP + 3 J cap + K cap and b vector is equal to 3 ICAP + 2 J cap + 4 k cap find out a + b vector into a minus b vector

Answer 1

you can see your answer

Answer 2

Answer: a+b vector into a-b vector is -18.

Explanation:

Given that,

$\vec{a}=\hat i+3\hat j+\hat k$

$\vec{b}=3\hat i+2\hat j+4\hat k$

Now,

$(\vec{a}+\vec{b})= (\hat i+3\hat j+\hat k)+(3\hat i+2\hat j+4\hat k)$

$(\vec{a}+\vec{b})=(4\hat i+5\hat j+5\hat k)$

$(\vec{a}-\vec{b})= (\hat i+3\hat j+\hat k)-(3\hat i+2\hat j+4\hat k)$

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

Now,

$(\vec{a}+\vec{b})\cdot (\vec{a}-\vec{b})= (4\hat i+5\hat j+5\hat k)\cdot (-2\hat i+\hat j-3\hat k)$

$(\vec{a}+\vec{b})\cdot (\vec{a}-\vec{b})=-18$

Hence, a+b vector into a-b vector is -18.