### Find the principal unit normal vector to the curve at the specified value of the parameter: R(t) = ti + (4/t)j where t=2

The question aims to find the unit normal vector to the curve at the specified value of the parameter. The question is based on the concept of vector geometry, tangent line, and normal vector. The tangent line is defined as a line that only passes through one point of the curve. The normal vector is […]

### Which of the following transformations are linear?

Verify which of the following transformations are linear. $T_1(x_1,x_2,x_3) = (x_1,0,x_3)$ $T_2(x_1,x_2)=(2x_1 – 3x_2,x_1 +4,5x_2)$ $T_3(x_1,x_2,x_3)=(1,x_2,x_3)$ $T_4(x_1,x_2)=(4x_1 – 2x_2,3|x_2|)$ $T_5(x_1,x_2,x_3)=(x_1,x_2,-x_3)$ The objective of this question is to find the linear transformation from the given transformation. Read moreFind a nonzero vector orthogonal to the plane through the points P, Q, and R, and area of the […]

### Find the dimension of the subspace spanned by the given vectors:

[ begin{bmatrix} 2 \ 4 \ 0 end{bmatrix} , begin{bmatrix} -1\ 6 \ 2 end{bmatrix} , begin{bmatrix} 1 \ 5 \ -3 end{bmatrix} , begin{bmatrix} 7 \ 2 \ 3 end{bmatrix} ] The question aims to find the dimension of the subspace spanned by the given column vectors. Read moreFind a nonzero vector orthogonal to […]

### Which of the following expressions are meaningful which are meaningless explain:

(a . b) . c (a . b) c |a|(b . c) a . (b + c) a . b + c |a| . (b+c) The questions aim to find the expressions of some vector multiplication and addition to check whether the expression is meaningful or meaningless. The background concept needed for this question to […]

### Find the scalar and vector projections of b onto a. a=i+j+k, b=i−j+k

The aim of this question is to find the Scalar and Vector Projection of the given two vectors. The basic concept behind this article is the understanding of Scalar and Vector Projections of vector quantities and how to calculate them. Read moreFind a nonzero vector orthogonal to the plane through the points P, Q, and […]