Question

if A=3i+j+2k and B=2i-2j+4k then the value of
$|a \times b|$
will be

Answer 1

hope it helps you ..........

Answer 2

Answer:

The magnitude of |a×b| is 8√3.

Explanation:

Given:

A = 3i + j + 2k

B = 2i - 2j + 4k

To find:

|a×b|

Solution:

a×b = $\left[\begin{array}{ccc}i&j&k\\a_1&a_2&a_3\\b_1&b_2&b_3\end{array}\right]$

From the given vectors A and B, we have a₁=3, a₂=1, a₃=2, b₁=2, b₂=-2, b₃=4.

Substituting the values in above formula, we get

a×b = $\left[\begin{array}{ccc}i&j&k\\3&1&2\\2&-2&4\end{array}\right]$

a×b = i[(1×4)-(2×-2)] - j[(3×4)-(2×2)] + k[(3×-2)-(2×1)]

a×b = i[4-(-4)] - j[12-4] + k[-6-2]

a×b = i(8) - j(8) + k(-8)

a×b = 8i - 8j - 8k

Now, to find the magnitude of a×b

|a×b| = $\sqrt{(a_1)^2+(a_2)^2+(a_3)^3}$

|a×b| = $\sqrt{(8)^2+(-8)^2+(-8)^2}$

|a×b| = $\sqrt{64+64+64}$

|a×b| = $\sqrt{192}$

|a×b| = 8√3

Therefore, the value of |a×b| is 8√3.

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