143602 Consider the vectors \(\mathbf{A}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, \quad \mathbf{B}=\) \(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\mathbf{C}=\frac{1}{\sqrt{5}}(\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}})\). What is the value of \(C .(A \times B)\) ?

143603 In a triangle \(\mathrm{ABC}\), the sides \(\mathrm{AB}\) and \(\mathrm{AC}\) are represented by the vectors \(3 \hat{i}+\hat{j}+\hat{k}\) and \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) respectively. Calculate the angle \(\angle \mathrm{ABC}\).

143604 Three vectors \(\mathbf{A}=\mathbf{a} \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}} ; \mathbf{B}=\hat{\mathbf{i}}+\mathbf{b} \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\mathbf{C}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\mathbf{c k}\) are mutually perpendicular \((\hat{\mathbf{i}}, \hat{\mathbf{j}}\) and \(\hat{k}\) are unit vectors along \(X, Y\) and \(Z\) - axis respectively). The respective values of \(a, b\) and c are

143605 \(\quad\) If \(\mathbf{A}=\mathbf{B}+\mathbf{C}\) have scalar magnitudes of \(5,4,3\) units respectively, then the angle between \(A\) and \(C\) is

143606 The magnitudes of vectors \(A, B\) and \(C\) are 3,4 and 5 units respectively. If \(A+B=C\), the angle between \(A\) and \(B\) is

143602 Consider the vectors \(\mathbf{A}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, \quad \mathbf{B}=\) \(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\mathbf{C}=\frac{1}{\sqrt{5}}(\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}})\). What is the value of \(C .(A \times B)\) ?

143603 In a triangle \(\mathrm{ABC}\), the sides \(\mathrm{AB}\) and \(\mathrm{AC}\) are represented by the vectors \(3 \hat{i}+\hat{j}+\hat{k}\) and \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) respectively. Calculate the angle \(\angle \mathrm{ABC}\).

143604 Three vectors \(\mathbf{A}=\mathbf{a} \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}} ; \mathbf{B}=\hat{\mathbf{i}}+\mathbf{b} \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\mathbf{C}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\mathbf{c k}\) are mutually perpendicular \((\hat{\mathbf{i}}, \hat{\mathbf{j}}\) and \(\hat{k}\) are unit vectors along \(X, Y\) and \(Z\) - axis respectively). The respective values of \(a, b\) and c are

143605 \(\quad\) If \(\mathbf{A}=\mathbf{B}+\mathbf{C}\) have scalar magnitudes of \(5,4,3\) units respectively, then the angle between \(A\) and \(C\) is

143606 The magnitudes of vectors \(A, B\) and \(C\) are 3,4 and 5 units respectively. If \(A+B=C\), the angle between \(A\) and \(B\) is

143602 Consider the vectors \(\mathbf{A}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, \quad \mathbf{B}=\) \(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\mathbf{C}=\frac{1}{\sqrt{5}}(\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}})\). What is the value of \(C .(A \times B)\) ?

143603 In a triangle \(\mathrm{ABC}\), the sides \(\mathrm{AB}\) and \(\mathrm{AC}\) are represented by the vectors \(3 \hat{i}+\hat{j}+\hat{k}\) and \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) respectively. Calculate the angle \(\angle \mathrm{ABC}\).

143604 Three vectors \(\mathbf{A}=\mathbf{a} \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}} ; \mathbf{B}=\hat{\mathbf{i}}+\mathbf{b} \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\mathbf{C}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\mathbf{c k}\) are mutually perpendicular \((\hat{\mathbf{i}}, \hat{\mathbf{j}}\) and \(\hat{k}\) are unit vectors along \(X, Y\) and \(Z\) - axis respectively). The respective values of \(a, b\) and c are

143605 \(\quad\) If \(\mathbf{A}=\mathbf{B}+\mathbf{C}\) have scalar magnitudes of \(5,4,3\) units respectively, then the angle between \(A\) and \(C\) is

143606 The magnitudes of vectors \(A, B\) and \(C\) are 3,4 and 5 units respectively. If \(A+B=C\), the angle between \(A\) and \(B\) is

143602 Consider the vectors \(\mathbf{A}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, \quad \mathbf{B}=\) \(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\mathbf{C}=\frac{1}{\sqrt{5}}(\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}})\). What is the value of \(C .(A \times B)\) ?

143603 In a triangle \(\mathrm{ABC}\), the sides \(\mathrm{AB}\) and \(\mathrm{AC}\) are represented by the vectors \(3 \hat{i}+\hat{j}+\hat{k}\) and \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) respectively. Calculate the angle \(\angle \mathrm{ABC}\).

143604 Three vectors \(\mathbf{A}=\mathbf{a} \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}} ; \mathbf{B}=\hat{\mathbf{i}}+\mathbf{b} \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\mathbf{C}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\mathbf{c k}\) are mutually perpendicular \((\hat{\mathbf{i}}, \hat{\mathbf{j}}\) and \(\hat{k}\) are unit vectors along \(X, Y\) and \(Z\) - axis respectively). The respective values of \(a, b\) and c are

143605 \(\quad\) If \(\mathbf{A}=\mathbf{B}+\mathbf{C}\) have scalar magnitudes of \(5,4,3\) units respectively, then the angle between \(A\) and \(C\) is

143606 The magnitudes of vectors \(A, B\) and \(C\) are 3,4 and 5 units respectively. If \(A+B=C\), the angle between \(A\) and \(B\) is

143602 Consider the vectors \(\mathbf{A}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, \quad \mathbf{B}=\) \(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\mathbf{C}=\frac{1}{\sqrt{5}}(\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}})\). What is the value of \(C .(A \times B)\) ?

143603 In a triangle \(\mathrm{ABC}\), the sides \(\mathrm{AB}\) and \(\mathrm{AC}\) are represented by the vectors \(3 \hat{i}+\hat{j}+\hat{k}\) and \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) respectively. Calculate the angle \(\angle \mathrm{ABC}\).

143604 Three vectors \(\mathbf{A}=\mathbf{a} \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}} ; \mathbf{B}=\hat{\mathbf{i}}+\mathbf{b} \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\mathbf{C}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\mathbf{c k}\) are mutually perpendicular \((\hat{\mathbf{i}}, \hat{\mathbf{j}}\) and \(\hat{k}\) are unit vectors along \(X, Y\) and \(Z\) - axis respectively). The respective values of \(a, b\) and c are

143605 \(\quad\) If \(\mathbf{A}=\mathbf{B}+\mathbf{C}\) have scalar magnitudes of \(5,4,3\) units respectively, then the angle between \(A\) and \(C\) is

143606 The magnitudes of vectors \(A, B\) and \(C\) are 3,4 and 5 units respectively. If \(A+B=C\), the angle between \(A\) and \(B\) is