Find the product (A Times B) Times c when, A = 2i + 2k, and B = -2i + 2k, C = 3j

Question

Find the product (A Times B) Times c when, A = 2i + 2k, and B = -2i + 2k, C = 3j + 3k A proton is accelerated from rest by a potential difference of 5000 V and an alpha particle is accelerate the potential difference of 10,000 Volts. What is the ratio V_a/V_P of their final speeds? An alpha particle and a mass of 4m_p. Two tiny non-conducting balls have identical charges of q = 3 nC (10^-9 C) and identical but unknown masses m. They are hanging in equilibrium from non-conducting threads of length L = 50 cm. Due to electrostatic repulsion the particles are separated from each other by a horizontal distance x = 2 cm. the angle theta is small enough so that its sine and tangent Calculate m, the mass of each ball, in grams.

Explanation / Answer

Option (c)-24i is the correct answer.

Explanation:

Given,

A = 2 i + 2 k ;

B = -2 i + 2 k ;

C = 3 j + 3 k

We need to determine (A x B) x C

A x B = (2 i + 2j) x (-2i + 2j)

A x B = i ( 0 - 0) + j (0 - 0) + k ( 4+4) = 0i + 0j + 8k

(A x B) x C = 8 k x (3 j + 3 k ) = i (0 - 24) + j (0 - 0 ) + k (0 - 0)

(A x B) x C = -24 i

Hence, Option (c)-24i is the correct answer.

[A humble request to you to put the other questions seperately. Let me know for any query.. Thanks].

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