Question Detail

PHY 101 PHY 101 Past Questions Objective Question
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Question

Given that A = 4i + 2k, B = -3i - 3k, and C = 6i - 4k. Find A · (B × C).
Options
A 7i - 5k
B -72i + 24k
C 0
Correct Answer
D 7i + 5k
Correct Answer

Option C is the correct answer.

Detailed Explanation

First, compute B × C. B = -3i + 0j - 3k, C = 6i + 0j - 4k. The cross product in determinant form: B × C = | i j k; -3 0 -3; 6 0 -4 | = i(0(-4) - (-3)0) - j((-3)(-4) - (-3)6) + k((-3)0 - 06) = i(0 - 0) - j(12 - (-18)) + k(0 - 0) = -j(12 + 18) = -30j. So B × C = -30j. Then A · (B × C) = (4i + 0j + 2k) · (-30j) = 40 + 0(-30) + 2*0 = 0.

Hint

First compute the cross product of B and C, then take the dot product of the result with A. Note that the scalar triple product is zero if the vectors are coplanar.

Question Info

Course: PHY 101
Topic: PHY 101 Past Questions
Type: Objective
Difficulty: Not specified
Question 1066 of 1250
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