The angle bisector a is parallel to λ ( b? +? ) or μ ( b? -? ). b? = (i+j)/√2 and? = (i-j+4k)/√ (1+1+16) = (i-j+4k)/ (3√2). Case 1: a = λ ( (i+j)/√2 + (i-j+4k)/ (3√2) ) a = λ/√2 * (3 (i+j) + (i-j+4k)/3 = λ/ (3√2) * (4i + 2j + 4k). a is given as αi + 2j + βk. Comparing the j-component: 2 = λ/ (3√2) * 2 ⇒ λ = 3√2. So, a = 1 * (4i + 2j + 4k) = 4i + 2j + 4k. Comparing with αi + 2j + βk, we get α = 4 and β = 4. (The image has a second case that needs evaluation as well). Case 2: a = μ ( b? -? ) a = μ/ (3&radi
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The angle bisector a is parallel to λ ( b? +? ) or μ ( b? -? ). b? = (i+j)/√2 and? = (i-j+4k)/√ (1+1+16) = (i-j+4k)/ (3√2). Case 1: a = λ ( (i+j)/√2 + (i-j+4k)/ (3√2) ) a = λ/√2 * (3 (i+j) + (i-j+4k)/3 = λ/ (3√2) * (4i + 2j + 4k). a is given as αi + 2j + βk. Comparing the j-component: 2 = λ/ (3√2) * 2 ⇒ λ = 3√2. So, a = 1 * (4i + 2j + 4k) = 4i + 2j + 4k. Comparing with αi + 2j + βk, we get α = 4 and β = 4. (The image has a second case that needs evaluation as well). Case 2: a = μ ( b? -? ) a = μ/ (3√2) * (3 (i+j) - (i-j+4k) = μ/ (3√2) * (2i + 4j - 4k). Comparing the j-component: 2 = μ/ (3√2) * 4 ⇒ 4μ = 6√2 ⇒ μ = 3√2/2. So, a = (3√2/2)/ (3√2) * (2i+4j-4k) = 1/2 * (2i+4j-4k) = I + 2j - 2k. This gives α=1, β=-2.
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<p>The angle bisector a is parallel to λ ( b? +? ) or μ ( b? -? ).<br>b? = (i+j)/√2 and? = (i-j+4k)/√ (1+1+16) = (i-j+4k)/ (3√2).<br>Case 1: a = λ ( (i+j)/√2 + (i-j+4k)/ (3√2) )<br>a = λ/√2 * (3 (i+j) + (i-j+4k)/3 = λ/ (3√2) * (4i + 2j + 4k).<br>a is given as αi + 2j + βk.<br>Comparing the j-component: 2 = λ/ (3√2) * 2 ⇒ λ = 3√2.<br>So, a = 1 * (4i + 2j + 4k) = 4i + 2j + 4k.<br>Comparing with αi + 2j + βk, we get α = 4 and β = 4.<br><em> (The image has a second case that needs evaluation as well)</em>.<br>Case 2: a = μ ( b? -? )<br>a = μ/ (3√2) * (3 (i+j) - (i-j+4k) = μ/ (3√2) * (2i + 4j - 4k).<br>Comparing the j-component: 2 = μ/ (3√2) * 4 ⇒ 4μ = 6√2 ⇒ μ = 3√2/2.<br>So, a = (3√2/2)/ (3√2) * (2i+4j-4k) = 1/2 * (2i+4j-4k) = I + 2j - 2k.<br>This gives α=1, β=-2.<br><!- [if !supportLineBreakNewLine]-></p>
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