Question

a vector is equal to 2 to ICAP Plus 3 j cap + 4 k cap and b vector is equal to minus two ICAP + 3 j cap - 4 k cap and c is equal to 4 ICAP + 7 j cap - 8 k cap find the component of a vector + b vector along c vector or find the projection of a vector + b vector on c vector​

Answer 1

Answer:

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

Explaination:

Given that,

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

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

Now,

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

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

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

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

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)(a+b)⋅(a−b)=(4i^+5j^+5k^)⋅(−2i^+j^−3k^)

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

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