87745 If \(\vec{a}\) and \(\vec{b}\) are the two vectors such that \(|\vec{a}|=3 \sqrt{3},|\vec{b}|=4\) and \(|\vec{a}+\vec{b}|=\sqrt{7}\), then the angle between \(\vec{a}\) and \(\vec{b}\) is

87746 If \(O(0,0,0), A(1,2,3), B(2,3,4)\) and \(C(x, y, z)\) are coplanar points, then which of the following is true?

87747 The area of a rhombus whose diagonals are \(\vec{a}=2 \hat{i}-3 \hat{j}+5 \vec{k}\) and \(\vec{b}=2 \hat{i}+2 \hat{j}+2 \hat{k}\) is

87748 Let
\(\overrightarrow{\mathbf{a}}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \overrightarrow{\mathbf{b}}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(\overrightarrow{\mathbf{c}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}\). A
vector in the plane of \(\vec{b}\) and \(\vec{c}\) whose projection on \(\vec{a}\) has the magnitude \(\sqrt{\frac{2}{3}}\), is

87745 If \(\vec{a}\) and \(\vec{b}\) are the two vectors such that \(|\vec{a}|=3 \sqrt{3},|\vec{b}|=4\) and \(|\vec{a}+\vec{b}|=\sqrt{7}\), then the angle between \(\vec{a}\) and \(\vec{b}\) is

87746 If \(O(0,0,0), A(1,2,3), B(2,3,4)\) and \(C(x, y, z)\) are coplanar points, then which of the following is true?

87747 The area of a rhombus whose diagonals are \(\vec{a}=2 \hat{i}-3 \hat{j}+5 \vec{k}\) and \(\vec{b}=2 \hat{i}+2 \hat{j}+2 \hat{k}\) is

87748 Let
\(\overrightarrow{\mathbf{a}}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \overrightarrow{\mathbf{b}}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(\overrightarrow{\mathbf{c}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}\). A
vector in the plane of \(\vec{b}\) and \(\vec{c}\) whose projection on \(\vec{a}\) has the magnitude \(\sqrt{\frac{2}{3}}\), is

87745 If \(\vec{a}\) and \(\vec{b}\) are the two vectors such that \(|\vec{a}|=3 \sqrt{3},|\vec{b}|=4\) and \(|\vec{a}+\vec{b}|=\sqrt{7}\), then the angle between \(\vec{a}\) and \(\vec{b}\) is

87746 If \(O(0,0,0), A(1,2,3), B(2,3,4)\) and \(C(x, y, z)\) are coplanar points, then which of the following is true?

87747 The area of a rhombus whose diagonals are \(\vec{a}=2 \hat{i}-3 \hat{j}+5 \vec{k}\) and \(\vec{b}=2 \hat{i}+2 \hat{j}+2 \hat{k}\) is

87748 Let
\(\overrightarrow{\mathbf{a}}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \overrightarrow{\mathbf{b}}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(\overrightarrow{\mathbf{c}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}\). A
vector in the plane of \(\vec{b}\) and \(\vec{c}\) whose projection on \(\vec{a}\) has the magnitude \(\sqrt{\frac{2}{3}}\), is

87745 If \(\vec{a}\) and \(\vec{b}\) are the two vectors such that \(|\vec{a}|=3 \sqrt{3},|\vec{b}|=4\) and \(|\vec{a}+\vec{b}|=\sqrt{7}\), then the angle between \(\vec{a}\) and \(\vec{b}\) is

87746 If \(O(0,0,0), A(1,2,3), B(2,3,4)\) and \(C(x, y, z)\) are coplanar points, then which of the following is true?

87747 The area of a rhombus whose diagonals are \(\vec{a}=2 \hat{i}-3 \hat{j}+5 \vec{k}\) and \(\vec{b}=2 \hat{i}+2 \hat{j}+2 \hat{k}\) is

87748 Let
\(\overrightarrow{\mathbf{a}}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \overrightarrow{\mathbf{b}}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(\overrightarrow{\mathbf{c}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}\). A
vector in the plane of \(\vec{b}\) and \(\vec{c}\) whose projection on \(\vec{a}\) has the magnitude \(\sqrt{\frac{2}{3}}\), is