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The angle between two planes is equal to the angle between their normal vectors. Normal vector of plane 1: n₁ = (1, −1, 1) Normal vector of plane 2: n₂ = (2, 1, −3) Use the formula: cos(θ) = |n₁ · n₂| / (||n₁|| · ||n₂||) Dot product: n₁ · n₂ = (1)(2) + (−1)(1) + (1)(−3) = 2 − 1 − 3 = −2 ⇒ |n₁ · n₂| = 2 Magnitude of n₁ = √(1² + (−1)² + 1²) = √3 Magnitude of n₂ = √(2² + 1² + (−3)²) = √14 cos(θ) = 2 / (√3 · √14) = 2 / √42 ⇒ θ = cos⁻¹(2 / √42)
Statements:
A > K ≥ M; Z ≤ A < T; C > M ≤ D
Conclusions:
I). Z < D
II). M < T
III). C < A
...Which of the following pairs represents the immediate neighbour of the one who do shopping from Limeroad?
Statements: L > M > P = N ≤ O ≤ Q, R > S = L
Conclusions:
I. P > S
II. Q ≥ M
III. N < S
Statements: F @ R, R $ J, V % J, V # Z
Conclusions: I. F * V II. R * V �...
Which of the following symbols should be placed in the blank spaces respectively (in the same order from left to right) in order to complete the given ...
Statement: X < V ≥ A > Y; A ≤ S < W
Conclusions:
I. X < W
II. S > Y
Statements: M % F & P % F; F # A & W; W @ O # S
Conclusions:
I. A @ O
II. M % O
III. S @ F
...Statements: F % W, W © R, R @ M, M $ D
Conclusions:
I.D @ R II.M $...
Statements: O ≥ M > F, K ≤ J ≤ D = F, B ≤ Z ≤ L = K
Conclusion:
I. M > L
II. D ≥ B
Statements: M % C & G @ T $ D; W % M # P
Conclusions : I. D % C II. M % G ...