Question

If P = 4.00î + 3.00k, P · Q = 17.0, and P ✕ Q = −6.00ĵ, determine the vector Q.

Answer 1

let the vector Q is given as

$\vec Q = a\hat i + b\hat j + c\hat k$

given that

$P X Q = -6\hat j$

here we know that

$P = 4\hat i + 3 \hatk$

now by above equation

$(4\hat i + 3\hat k) X (a\hat i + b\hat j + c\hat k) = - 6\hat j$

$4b\hat k - 4c\hat j + 3a\hat j - 3b\hat i = - 6\hat j$

so by comparing both sides

b = 0

4c - 3a = 6

also we know that

$a^2 + b^2 + c^2 = 17^2$

$a^2 + 0 + (1.5 + 0.75a)^2 = 289$

by solving above equation

a = 12.85 and c = 11.14

so the vector Q is given as

$Q = 12.85\hat i + 11.14\hat k$