Question

value of :
a) (ixj).k+i.j
b) (j×k).i+(i×k).j+(i×j).k
​

Answer 1

To Find:

The value of,

ㅤ(a)ㅤ(i × j) • k + i • j

ㅤ(b)ㅤ(j × k) • i + (i × k) • j + (i × j) • k

Solving the question:

ㅤ(a)ㅤ(i × j) • k + i • j

Solⁿ:

ㅤ=ㅤk • k + i • j

ㅤ=ㅤ| k |² + 0

ㅤ=ㅤ| k |²

ㅤ=ㅤ1

ㅤ(b)ㅤ(j × k) • i + (i × k) • j + (i × j) • k

Solⁿ:

ㅤ=ㅤi • i + (- j) • j + k • k

ㅤ=ㅤ| i |² - | j |² + | k |²

ㅤ=ㅤ1 - 1 + 1

ㅤ=ㅤ1

Some vectors formula:

• i × j = k
• j × k = i
• k × i = j
• j × i = - k
• k × j = - i
• i × k = - j
• i • j = j • i = 0
• j • k = k • j = 0
• k • i = i • k = 0
• i • i = | i |² = 1
• j • j = | j |² = 1
• k • k = | k |² = 1