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8. Suppose I is a triangle formed by placing three points lircle, two of which lie on the circle's diameter. Ube on a the previous problem to show I is a right triangle.

8. Suppose I is a triangle formed by placing three points lircle, two of which lie on the circle's diameter. Ube on a the previous problem to show I is a right triangle.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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8. Suppose I is a triangle formed by placing three points circle, two of which lie on the circle's diameter. Use the previous problem to show I is a right triangle. on a XXX Xper 3-4 nitiat
Transcribed Image Text:8. Suppose I is a triangle formed by placing three points circle, two of which lie on the circle's diameter. Use the previous problem to show I is a right triangle. on a XXX Xper 3-4 nitiat
congle. Given that V₁W € Rn and 1||v|| = ||w|l. We have to show that vtw and v-w are orthogonal *Orthogonal vectors: Let V be an inner product space and orthogonal if (UV ro U₁vbe vectors in V. Then vand v are * properties: Let V be an inner product space them for all virwEv hove ille (i) (ut V₁06) = (v₁ ) + (1₁0) (ii) (v₁v-w) = (U₁V) - (U₁0) *If v be an real inner product space, then (U,V) = (V₁U) for all v₁V E Ve * Norm of a vector: Letv be an inner product space and VEV. Then norm of v, denoted by IVII, is defined as 11V1= 5 Note: As per our quidelines. we are supposed to solve the STVU) that EIR and 11v11 = ||w|l. first one only, Hene given v, w Now, (V+∞, v-w) = (v₁ V-) + (W₁V-W) = (v₁v) - (V₁w) + (w, v) - (W₁w) = || v11 ² - (V₁W) + (v₁w) - || || ² 2 = || v || ²_ ||w| || ² 2 = || V || ² - Il vii" real inner is al product space, (WV) = (v₁) And 11 vil = √(V₁V). i.e. (V+W₁v-w)=0XE =J Vtw and v- ore Hence, vtw and v-c are IR [: || | || = ||||| orthogonal. n orthogonal ~(2)9
Transcribed Image Text:congle. Given that V₁W € Rn and 1||v|| = ||w|l. We have to show that vtw and v-w are orthogonal *Orthogonal vectors: Let V be an inner product space and orthogonal if (UV ro U₁vbe vectors in V. Then vand v are * properties: Let V be an inner product space them for all virwEv hove ille (i) (ut V₁06) = (v₁ ) + (1₁0) (ii) (v₁v-w) = (U₁V) - (U₁0) *If v be an real inner product space, then (U,V) = (V₁U) for all v₁V E Ve * Norm of a vector: Letv be an inner product space and VEV. Then norm of v, denoted by IVII, is defined as 11V1= 5 Note: As per our quidelines. we are supposed to solve the STVU) that EIR and 11v11 = ||w|l. first one only, Hene given v, w Now, (V+∞, v-w) = (v₁ V-) + (W₁V-W) = (v₁v) - (V₁w) + (w, v) - (W₁w) = || v11 ² - (V₁W) + (v₁w) - || || ² 2 = || v || ²_ ||w| || ² 2 = || V || ² - Il vii" real inner is al product space, (WV) = (v₁) And 11 vil = √(V₁V). i.e. (V+W₁v-w)=0XE =J Vtw and v- ore Hence, vtw and v-c are IR [: || | || = ||||| orthogonal. n orthogonal ~(2)9
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