Let `veca=hati-hatj+hatk, vecb=2hati+hatj` and `vecc=3hatj-2hatk,vecx,vecy,vecz` be linear combination of `veca,vecb,vecb,vecc,vecc,veca` respectively and `vecr=lamdavecx+muvecy+deltavecz,lamda,mu,delta` are some scalars. If `vecd` is equally inclined to three vectors `veca,vecb,vecc` then

Options

A. a. `vecx.vecd=14`
B. b. `vecy.vecd=3`
C. c. `vecz.vecd=0`
D. d. `vecr.vecd=0`

Explanation

To solve the problem, we need to find the vector \(\vec{d}\) that is equally inclined to the vectors \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\). Let's go through the steps systematically.

### Step 1: Define the vectors
We are given the following vectors:
- \(\vec{a} = \hat{i} - \hat{j} + \hat{k}\)
- \(\vec{b} = 2\hat{i} + \hat{j}\)
- \(\vec{c} = 3\hat{j} - 2\hat{k}\)

...