Question

Find the value of (4i^ )× ( -6k^ )

Answer 1

As this question is about vector cross product
according to some general rules
a)i^×j^=k^
b)j^×k^=i^
c)k^×i^=j^
again if the multiplication is in opposite of this rule then a minus sign will be given to the resultant
so in your question 4i^×(-6k^)=24j^
as vector multiplication is in opposite so additional minus sign is introduced

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hope it will help you

Answer 2

!! Hey Mate !!

your answer is --

Let, A = 4i^ and B = (-6k^)

we can write it as

A = 4i^ + 0j^ + 0k^ and

B = 0i^ +0j^ - 6k^

such that , a1 = 4 , a2=0, a3=0 and

b1 = 0 , b2 = 0 , b3= -6

we know that ,

A × B = i^(a2b3-b2a3) - j^(a1b3-b1a3) +k^(a1b2-b1a2)

=> A×B = i^(0×-6-0×4)-j^(4×-6-0×0)+k^(4×0-0×0)

=> A×B = i^(0) - j^(-24) +k^(0)

=> A×B = 24j^

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Alternate method

we know that

k^ + i^ = j^

=> -6k^ × 4i^ = 24j^


【 Hope it helps you 】